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A325069
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Prime numbers congruent to 9 modulo 16 representable by x^2 + 32*y^2.
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3
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41, 137, 313, 409, 457, 521, 569, 761, 809, 857, 953, 1129, 1321, 1657, 1993, 2137, 2153, 2297, 2377, 2521, 2617, 2633, 2713, 2729, 2777, 2953, 3001, 3209, 3433, 3593, 3769, 3881, 3929, 4073, 4441, 4649, 4729, 4793, 4889, 4969, 5273, 5417, 5449, 5641, 5657
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Kaplansky showed that prime numbers congruent to 9 modulo 16 are representable by exactly one of the quadratic forms x^2 + 32*y^2 or x^2 + 64*y^2. This sequence corresponds to those representable by the first form and A325070 to those representable by the second form.
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LINKS
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EXAMPLE
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Regarding 41:
- 41 is a prime number,
- 41 = 2*16 + 9,
- 41 = 3^2 + 32*1^2,
- hence 41 belongs to this sequence.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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