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Search: id:A080169
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| A080169 |
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Cube of a prime of the form 4n+1 which is the hypotenuse of three and only three right triangles with integral arms. |
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| 125, 2197, 4913, 24389, 50653, 68921, 148877, 226981, 389017, 704969, 912673, 1030301, 1295029, 1442897, 2571353, 3307949, 3869893, 5177717, 5929741, 7189057, 7645373, 12008989, 12649337, 13997521, 16974593, 19465109, 21253933
(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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2197 is the hypotenuse of triangles 825, 2035, 2197; 845, 2028, 2197; 1547, 1560, 2197.
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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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Sequence in context: A030082 A017043 A102061 this_sequence A017127 A119633 A017223
Adjacent sequences: A080166 A080167 A080168 this_sequence A080170 A080171 A080172
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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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