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A270698
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Composite numbers k == 1 (mod 4) such that (1 + i)^k == 1 + i (mod k), where i = sqrt(-1).
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6
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561, 1105, 1729, 1905, 2465, 3277, 4033, 4681, 6601, 8321, 8481, 10585, 12801, 15841, 16705, 18705, 25761, 29341, 30121, 33153, 34945, 41041, 46657, 49141, 52633, 62745, 65281, 74665, 75361, 80581, 85489, 87249, 88357, 104653, 113201, 115921, 126217, 129921
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OFFSET
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1,1
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COMMENTS
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Numbers in A047713 that are congruent to 1 mod 4. Most terms are congruent to 1 mod 8. For terms congruent to 5 mod 8, see A244626.
Also composite k == 1 (mod 4) such that (-4)^((k-1)/4) == 1 (mod k). Note that this is satisfied by all primes == 1 (mod 4), see A318898. (End)
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LINKS
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MATHEMATICA
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Select[1 + 4*Range[100000], PrimeQ[#] == False && PowerMod[1 + I, #, #] == 1 + I &]
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PROG
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(PARI) forstep(n=5, 10^5, 4, if(Mod(2, n)^((n-1)/2)==kronecker(2, n) && !isprime(n), print1(n, ", "))) \\ Jianing Song, Sep 06 2018
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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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