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 A002314 Minimal integer square root of -1 modulo p, where p is the n-th prime of the form 4k+1. (Formerly M1314 N0503) 18
 2, 5, 4, 12, 6, 9, 23, 11, 27, 34, 22, 10, 33, 15, 37, 44, 28, 80, 19, 81, 14, 107, 89, 64, 16, 82, 60, 53, 138, 25, 114, 148, 136, 42, 104, 115, 63, 20, 143, 29, 179, 67, 109, 48, 208, 235, 52, 118, 86, 24, 77, 125, 35, 194, 154, 149, 106, 58, 26, 135, 96, 353, 87, 39 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In other words, if p is the n-th prime == 1 (mod 4), a(n) is the smallest positive integer k such that k^2 + 1 == 0 (mod p). The 4th roots of unity mod p, where p = n-th prime == 1 (mod 4), are +1, -1, a(n) and p-a(n). Related to Stormer numbers. Comment from Igor Shparlinski, Mar 12 2007 (writing to the Number Theory List): Results about the distribution of roots (for arbitrary quadratic polynomials) are given by W. Duke, J. B. Friedlander and H. Iwaniec and A. Toth. Comment from Emmanuel Kowalski, Mar 12 2007 (writing to the Number Theory List): It is known (Duke, Friedlander, Iwaniec, Annals of Math. 141 (1995)) that the fractional part of a(n)/p(n) is equidistributed in [0,1/2] for p(n)

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Last modified May 14 16:17 EDT 2021. Contains 343884 sequences. (Running on oeis4.)