Des Triplets Pythagoriciens

'____________________________________________________
' Les sommes des puissances des coefficients binomiaux
' des diagonales principales du Triangle de Pascal
'_________________________
' mathématiques récréatives
'_________________________
'
'
'_____________________________
'______________h^2 = a^2+b^2
'
' LES TRIPLETS PYTHAGORICIENS
'_______________________________________________lundi 4 août 1997_______
'
' où : h, a et b sont des entiers
' --
' h est premier
' [ h = hypoténuse ]
' a est impair
' [ et quelquefois premier: "a-" ]
' b est pair et multiple de 4
'_______________________________________________________________________________
'__rang____rang de h_________h________________a_______________b
'__________comme premier__(premier)_________(impair)_________(pair)
'____________________________________________________________________________
'____1__________3___________5________________3-______________4
'____2__________6__________13________________5-_____________12
'____3__________7__________17_______________15_______________8
'____4_________10__________29_______________21______________20
'____5_________12__________37_______________35______________12
'____6_________13__________41________________9______________40
'____7_________16__________53_______________45______________28
'____8_________18__________61_______________11-_____________60
'____9_________21__________73_______________55______________48
'___10_________24__________89_______________39______________80
'___11_________25__________97_______________65______________72
'___12_________26_________101_______________99______________20
'___13_________29_________109_______________91______________60
'___14_________30_________113_______________15_____________112
'___15_________33_________137______________105______________88
'___16_________35_________149_______________51_____________140
'___18_________40_________173______________165______________52
'___19_________42_________181_______________19-____________180
'___20_________44_________193_______________95_____________168
'___21_________45_________197______________195______________28
'___22_________50_________229______________221______________60
'___23_________51_________233______________105_____________208
'___24_________53_________241______________209_____________120
'___25_________55_________257______________255______________32
'___26_________57_________269_______________69_____________260
'___27_________59_________277______________115_____________252
'___28_________60_________281______________231_____________160
'___29_________62_________293______________285______________68
'___30_________65_________313_______________25_____________312
'___31_________66_________317_______________75_____________308
'___32_________68_________337______________175_____________288
'___33_________70_________349______________299_____________180
'___34_________71_________353______________225_____________272
'___35_________74_________373______________275_____________252
'___36_________77_________389______________189_____________340
'___37_________78_________397______________325_____________228
'___38_________79_________401______________399______________40
'___39_________80_________409______________391_____________120
'___40_________82_________421_______________29-____________420
'___41_________84_________433______________145_____________408
'___42_________87_________449______________351_____________280
'___43_________88_________457______________425_____________168
'___44_________89_________461______________261_____________380
'___45_________97_________509______________459_____________220
'___46_________98_________521______________279_____________440
'___47________100_________541______________341_____________420
'___48________102_________557______________165_____________532
'___49________104_________569______________231_____________520
'___50________106_________577______________575______________48
'___51________108_________593______________465_____________368
'___52________110_________601______________551_____________240
'___53________112_________613_______________35_____________612
'___54________113_________617______________105_____________608
'___55________116_________641______________609_____________200
'___56________119_________653______________315_____________572
'___57________121_________661______________589_____________300
'___58________122_________673______________385_____________552
'___59________123_________677______________675______________52
'___60________126_________701______________651_____________260
'___61________127_________709______________259_____________660
'___62________130_________733______________725_____________108
'___63________134_________757______________595_____________468
'___64________135_________761_______________39_____________760
'___65________136_________769______________481_____________600
'___66________137_________773______________195_____________748
'___67________139_________797______________555_____________572
'___68________140_________809______________759_____________280
'___69________142_________821______________429_____________700
'___70________145_________829______________629_____________540
'___71________147_________853______________205_____________828
'___72________148_________857______________825_____________232
'___73________151_________877______________805_____________348
'___74________152_________881______________369_____________800
'___75________158_________929______________129_____________920
'___76________159_________937______________215_____________912
'___77________160_________941______________741_____________580
'___78________162_________953______________615_____________728
'___79________165_________977______________945_____________248
'___80________168_________997______________925_____________372
'___81________169________1009______________559_____________840
'___82________170________1013_______________45____________1012
'___83________172________1021______________779_____________660
'___84________174________1033_____________1015_____________192
'___85________176________1049______________999_____________320
'___86________178________1061______________861_____________620
'___87________180________1069______________731_____________780
'___88________183________1093_____________1085_____________132
'___89________184________1097______________585_____________928
'___90________186________1109______________141____________1100
'___91________187________1117______________235____________1092
'___92________189________1129______________329____________1080
'___93________191________1153_____________1025_____________528
'___94________194________1181_____________1131_____________340
'___95________196________1193______________855_____________832
'___96________197________1201_______________49____________1200
'___97________198________1213______________245____________1188
'___98________199________1217______________705_____________992
'___99________201________1229_____________1221_____________140
'__100________203________1237_____________1075_____________612
'__101________204________1249______________799_____________960
'__102________206________1277_____________1035_____________748
'__103________209________1289_____________1161_____________560
'__104________211________1297_____________1295______________72
'__105________212________1301_______________51____________1300
'__106________216________1321_____________1271_____________360
'__107________218________1361______________561____________1240
'__108________220________1373_____________1365_____________148
'__109________221________1381______________931____________1020
'__110________223________1409______________159____________1400
'__111________226________1429______________371____________1380
'__112________227________1433_____________1305_____________592
'__113________231________1453_____________1435_____________228
'__114________234________1481______________969____________1120
'__115________237________1489______________689____________1320
'__116________238________1493_____________1395_____________532
'__117________244________1549______________901____________1260
'__118________245________1553______________495____________1472
'__119________251________1597______________715____________1428
'__120________252________1601_____________1599______________80
'__121________254________1609_____________1591_____________240
'__122________255________1613_____________1275_____________988
'__123________257________1621_____________1421_____________780
'__124________259________1637______________285____________1612
'__125________260________1657______________935____________1368
'__126________263________1669_____________1219____________1140
'__127________264________1693_____________1045____________1332
'__128________265________1697_____________1665_____________328
'__129________267________1709______________741____________1540
'__130________268________1721_____________1479_____________880
'__131________270________1733_____________1155____________1292
'__132________271________1741_______________59-___________1740
'__133________273________1753______________295____________1728
'__134________275________1777_____________1265____________1248
'__135________278________1789_____________1739_____________420
'__136________279________1801______________649____________1680
'__137________284________1861_______________61-___________1860
'__138________287________1873______________305____________1848
'__139________288________1877_____________1485____________1148
'__140________290________1889_____________1311____________1360
'__141________291________1901______________549____________1820
'__142________293________1913_____________1785_____________688
'__143________295________1933_____________1595____________1092
'__144________296________1949_____________1749_____________860
'__145________298________1973______________915____________1748
'__146________301________1993_____________1705____________1032
'__147________302________1997______________315____________1972
'__148________306________2017_____________1855_____________792
'__149________308________2029_____________2021_____________180
'__150________310________2053_____________1475____________1428
'__151________312________2069______________819____________1900
'__152________313________2081_____________1281____________1640
'__153________316________2089_____________1961_____________720
'__154________319________2113_______________65____________2112
'__155________320________2129_____________1071____________1840
'__156________322________2137______________455____________2088
'__157________323________2141_____________2091_____________460
'__158________325________2153______________585____________2072
'__159________326________2161_____________1711____________1320
'__160________330________2213_____________2205_____________188
'__161________331________2221_____________1829____________1260
'__162________332________2237_____________1995____________1012
'__163________337________2269______________469____________2220
'__164________338________2273_____________2145_____________752
'__165________339________2281_____________1769____________1440
'__166________341________2293_____________1235____________1932
'__167________342________2297_____________1575____________1672
'__168________343________2309_____________2109_____________940
'__169________345________2333_____________1365____________1892
'__170________347________2341_____________1891____________1380
'__171________350________2357_____________1005____________2132
'__172________352________2377_____________1495____________1848
'__173________353________2381_______________69____________2380
'__174________355________2389_____________1139____________2100
'__175________356________2393______________345____________2368
'__176________359________2417_____________2385_____________392
'__177________361________2437_____________2365_____________588
'__178________362________2441______________759____________2320
'__179________366________2473_____________2135____________1248
'__180________367________2477_____________1755____________1748
'__181________369________2521_______________71-___________2520
'__182________373________2549_____________2451_____________700
'__183________375________2557_____________1675____________1932
'__184________378________2593_____________2015____________1632
'__185________379________2609_____________1809____________1880
'__186________380________2617_____________2585_____________408
'__187________381________2621_____________2379____________1100
'__188________382________2633_____________1065____________2408
'__189________384________2657_____________2145____________1568
'__190________388________2677______________365____________2652
'__191________391________2689______________511____________2640
'__192________392________2693_____________1725____________2068
'__193________396________2713_____________2695_____________312
'__194________398________2729_____________2679_____________520
'__195________400________2741_____________1491____________2300
'__196________401________2749______________949____________2580
'__197________402________2753_____________2655_____________728
'__198________404________2777_____________1095____________2552
'__199________405________2789_____________2211____________1700
'__200________407________2797_____________2405____________1428
'__201________408________2801_____________2001____________1960
'__202________411________2833_____________1775____________2208
'__203________412________2837______________525____________2788
'__204________415________2857_____________2345____________1632
'__205________416________2861_____________2139____________1900
'__206________419________2897______________975____________2728
'__207________421________2909_____________2709____________1060
'__208________422________2917_____________2915_____________108
'__209________425________2953_____________2665____________1272
'__210________426________2957_____________1275____________2668
'__211________428________2969______________231____________2960
'__212________431________3001_____________2201____________2040
'__213_________..._________...._______________...._____________....
'__214_________..._________...._______________...._____________....
'__215_________..._________...._______________...._____________....
'___..._________..._________...._______________...._____________....
'___..._________..._________...._______________...._____________....
'___..._________..._________...._______________...._____________....
'

'
'_________________________________________________________________________
'_____________*** Certains triplets intéressants ***____________________
'_________________________________________________________________________
'____1__________3___________5________________3-______________4
'____2__________6__________13________________5-_____________12
'____8_________18__________61_______________11-_____________60
'___19_________42_________181_______________19-____________180
'___40_________82_________421_______________29-____________420
'__132________271________1741_______________59-___________1740
'__137________284________1861_______________61-___________1860
'__181________369________2521_______________71-___________2520
'__..._________445________3121_______________79-___________3120
'__..._________682________5101______________101-___________5100
'__...________1069________8581______________131-___________8580
'__...________1193________9661______________139-___________9660
'__...________1900_______16381______________181-__________16380
'__...________2241_______19801______________199-__________19800
'__...________3894_______36721______________271-__________36720
'__...________6137_______60901______________349-__________60900
'__...________7108_______71821______________379-__________71820
'__...________8164_______83641______________409-__________83640
'__...________9658______100801______________449-_________100800
'__..._______10126______106261______________461-_________106260
'__..._______12645______135721______________521-_________135720
'__..._______14842______161881______________569-_________161880
'__..._______14936______163021______________571-_________163020
'__..._______17913______199081______________631-_________199080
'__..._______18420______205441______________641-_________205440
'__..._______19480______218461______________661-_________218460
'__..._______23893______273061______________739-_________273060
'__..._______24605______282001______________751-_________282000
'__..._______28959______337021______________821-_________337020
'__..._______32913______388081______________881-_________388080
'__..._______36279______431521______________929-_________431520
'__..._______40847______491041______________991-_________491040
'__..._______43936______531481_____________1031-_________531480
'__..._______44559______539761_____________1039-_________539760
'__..._______45500______552301_____________1051-_________552300
'__..._______46932______571381_____________1069-_________571380
'__..._______48740______595141_____________1091-_________595140
'__..._________...._______637321_____________1129-_________637320
'__..._________...._______662401_____________1151-_________662400
'__..._________...._______685621_____________1171-_________685620
'__..._________...._______697381_____________1181-_________697380
'__..._________...._______926161_____________1361-_________926160
'__..._________....______1035361_____________1439-________1035360
'__..._________....______1064341_____________1459-________1064340
'__..._________....______1108561_____________1489-________1108560
'__..._________....______1123501_____________1499-________1123500
'__..._________....______1171981_____________1531-________1171980
'__..._________....______1460341_____________1709-________1460340
'__..._________....________......_______________....-____________......
'__..._________....________......_______________....-____________......
'__..._________....________......_______________....-____________......
'__..._________....________......_______________....-____________......
'__..._________....________......_______________....-____________......
'
'
'
'_____________13^2__=___3^2___+4^2____+12^2
'____________421^2__=__20^2__+21^2___+420^2
'___________1861^2__=__11^2__+60^2__+1860^2
'___________5101^2__=__20^2__+99^2__+5100^2
'_______________________________________________________________________________
'______________________[ pythagor.txt, 51439 octets, 1997-08-04, 0:27 ]
'_______________________________________________________________________________
'
'
'
'===============================================================================
'   Liste de quelques bons auteurs
'   ayant écrit ou inventé
'   sur les triplets pythagoriciens :
'
'
'
' - Fred Curtiss' Primitive Pythagorean Triples Page
'
'
' - Terry Dash (Making Mathematics : Pythagorean Triples :
'____________________________________________________Resources)
'________________________(Education Development Center, Inc. {EDC})
'
'
' - Harvey Dubner
'__[ Harvey Dubner and Tony Forbes, Prime Pythagorean triangles,
'________{ Primes of the Form (b^n+1)/(b+1) } Journal of Integer
'_____________________Sequences, Vol. 4 (2001), Article 01.2.3 ]
'
'
' - Ernest J. Eckert (Primitive Pythagorean Triples, The College
'____________________________Mathematics Journal, 23: 413-417, 1992)
'
'
' - Stuart M. Ellerstein
'_[ "Square Spiral", J. Recr. Math., 1999-2000, 30(4): 246-250 ]
'_[ "The Pronic Renaissance: The Ulam Square Spiral
'___(Modified)." J. Recr. Math. 29, 188-189, 1998 ]

' [ Prime Spiral - Wolfram ]

'______________________http://mathworld.wolfram.com/PrimeSpiral.html

'
'
' - William Richardson's page
'
'
' - Eric S. Rowland (Eric Rowland's page)

' [ Triples ]

'__________________http://people.ucsc.edu/~erowland/powers.html

' - Neil James Alexander Sloane's Home Page

' Editor (2003), The On-Line Encyclopedia of Integer Sequences

' [ OEIS ]

'__________________http://www.research.att.com/~njas/sequences/

'_____________________________________________

'_____________________________________________________________

'
'
' - Eric W. Weisstein (Eric Weisstein's World of Mathematics)

' [ MathWorld ]

'_____________________________________http://mathworld.wolfram.com/

'
'
'