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Search: id:A107961
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| A107961 |
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Pythagorean semiprimes: products of two Pythagorean primes (A002313). |
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+0
1
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| 4, 10, 25, 26, 34, 58, 65, 74, 82, 85, 106, 122, 145, 146, 169, 178, 185, 194, 202, 205, 218, 221, 226, 265, 274, 289, 298, 305, 314, 346, 362, 365, 377, 386, 394, 445, 458, 466, 481, 482, 485, 493, 505, 514, 533, 538, 545, 554, 562, 565, 586, 626, 629, 634
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique manner (up to the order of addends) in the form x^2 + y^2 for integer x and y iff p = 1 (mod 4) or p = 2 (which is a degenerate case with x = y = 1). The theorem was stated by Fermat, but the first published proof was by Euler.
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REFERENCES
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Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 146-147 and 220-223, 1996.
Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 13 and 219, 1979.
Seroul, R. "Prime Number and Sum of Two Squares." Section 2.11 in Programming for Mathematicians. Berlin: Springer-Verlag, pp. 18-19, 2000.
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LINKS
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Eric Weisstein's World of Mathematics, Fermat's 4n Plus 1 Theorem.
Eric Weisstein's World of Mathematics, Semiprime.
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FORMULA
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{a(n)} = {p*q: p and q both elements of A002313} = {p*q: p and q both of form m^2 + n^2 for integers m, n}.
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CROSSREFS
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Cf. A001358, A002313, A002330, A002331.
Adjacent sequences: A107958 A107959 A107960 this_sequence A107962 A107963 A107964
Sequence in context: A001868 A038783 A127070 this_sequence A051864 A111153 A111207
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Jun 12 2005
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