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Search: id:A080175
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| A080175 |
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Fourth power of a prime of the form 4n+1 which is the hypotenuse of four and only four right triangles with integral arms. |
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+0
2
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| 625, 28561, 83521, 707281, 1874161, 2825761, 7890481, 13845841, 28398241, 62742241, 88529281, 104060401, 141158161, 163047361, 352275361, 492884401, 607573201, 895745041, 1073283121, 1387488001, 1506138481, 2750058481
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In 1640 Fermat generalized the 3,4,5 triangle with the theorem: A prime of the form 4n+1 is the hypotenuse of one and only one right triangle with integral arms. The square of 4n+1 is the hypotenuse of two and only two...The cube of three and only three...
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REFERENCES
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Morris Kline, Mathematical Thought from Ancient to Modern Times, 1972, pp. 275-276.
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EXAMPLE
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625 is the hypotenuse of triangles 175, 600, 625; 220, 585, 625; 336, 527, 685; 375, 500, 625.
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PROGRAM
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(PARI) fermat(n) = { for(x=1, n, y=4*x+1; if(isprime(y), print1(y^3" ")) ) }
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CROSSREFS
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Adjacent sequences: A080172 A080173 A080174 this_sequence A080176 A080177 A080178
Sequence in context: A016852 A016972 A017044 this_sequence A017128 A017224 A017332
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Mar 16 2003
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