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Search: id:A059771
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| A059771 |
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Second solution of x^2 = 2 mod p for primes p such that a solution exists. |
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+0
3
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| 0, 4, 11, 18, 23, 24, 40, 59, 41, 70, 64, 83, 65, 62, 111, 106, 105, 154, 134, 141, 179, 208, 148, 140, 219, 197, 153, 175, 149, 245, 193, 311, 186, 340, 288, 246, 348, 312, 243, 227, 418, 419, 377, 260, 292, 396, 346, 272, 368, 543, 451, 433, 379, 413, 321
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Solutions mod p are represented by integers from 0 to p-1. For p > 2: If x^2 = 2 has a solution mod p, then it has exactly two solutions and their sum is p; i is a solution mod p of x^2 = 2 iff p-i is a solution mod p of x^2 = 2. No integer occurs more than once in this sequence. Moreover, no integer (except 0) occurs both in this sequence and in sequence A059770 of the first solutions (Cf. A059772).
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FORMULA
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a(n) = second (larger) solution of x^2 = 2 mod p, where p is the n-th prime such that x^2 = 2 mod p has a solution, i.e. p is the n-th term of A038873. a(n) = 0 if x^2 = 2 mod p has one solution (only for p = 2).
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EXAMPLE
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a(6) = 24 since 41 is the sixth term of A038873, 17 and 24 are the solutions mod 41 of x^2 = 2 and 24 is the larger one.
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CROSSREFS
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A038873, A059770, A059772.
Sequence in context: A063556 A133725 A050395 this_sequence A043409 A030610 A003327
Adjacent sequences: A059768 A059769 A059770 this_sequence A059772 A059773 A059774
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 21 2001
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