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 A065903 Integers i > 1 for which there is no prime p such that i is a solution mod p of x^4 = 2. 6
 1689, 1741, 3306, 3894, 4362, 4587, 4999, 5754, 6025, 6371, 6668, 7012, 7982, 9054, 9158, 9695, 9742, 9832, 10056, 10664, 11005, 12027, 12385, 13676, 13895, 14026, 14059, 16104, 16239, 16903, 17050, 17153, 18079, 18202, 18642, 20349, 21060 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Solutions mod p are represented by integers from 0 to p-1. The following equivalences holds for i > 1: There is a prime p such that i is a solution mod p of x^4 = 2 iff i^4 - 2 has a prime factor > i; i is a solution mod p of x^4 = 2 iff p is a prime factor of i^4 - 2 and p > i. i^4 - 2 has at most three prime factors > i. For i such that i^4 - 2 has one resp. two resp. three prime factors > i; cf. A065904 resp. A065905 resp. A065906. LINKS FORMULA a(n) = n-th integer i such that i^4 - 2 has no prime factor > i. EXAMPLE a(2) = 1741, since 1741 is (after 1689) the second integer i for which there are no primes p > i such that i is a solution mod p of x^4 = 2, or equivalently, 1741^4 - 2 = 9187452028559 = 7*7*79*887*1609*1663 has no prime factor > 1741. (cf. A065902). PROG (PARI): a065903(m) = local(c, n, f, a); c = 0; n = 2; while(c

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Last modified June 12 16:55 EDT 2021. Contains 344959 sequences. (Running on oeis4.)