# nonresidue

## nonresidue

[‚nän′rez·ə‚dü]
(mathematics)
A nonresidue of m of order n, where m and n are integers, is an integer a such that x n = a + bm, where x and b are integers, has no solution.
References in periodicals archive ?
2d]P [member of] G}, d | p + 1, a a quadratic nonresidue of [Z.
Otherwise a is quadratic nonresidue modulo n and denoted as a [member of] [bar.
Hereafter referred to as nonresidue, Flemingia leaf, medic hay, and wheat straw, respectively.
At the 48-day harvest, application of medic hay, Flemingia leaf, and wheat straw in the presence of N alone produced increased plant top yield compared with the nonresidue control.
The main result of Graham and Ringrose  asserts that for infinitely many primes p, the smallest quadratic nonresidue modulo p is at least [Omega](log p log log log p) (this result holds for primes p [equivalent] 3 (mod 4) as well, as follows from the remark at the end of Graham and Ringrose ).
n] + 1/179) = -1, since 128, 105 and 53 are quadratic nonresidues modulo 179, so that we can eliminate n [equivalent to] 15, 25 and 51 (mod 72).
49] + 1 [equivalent to] 62, 52, 62 or 31 (mod 73), by Table 3(a) and all of them are quadratic nonresidues modulo 73.
n] + 1 [equivalent to] 73, 70, 71, 15, 15, 29, 71, 70, 307, 267, 266, 314, 314, 266, 267, 307, 269, 268, 29, 268, 269, 73 or 314 (mod 337) respectively, and all of them are quadratic nonresidues modulo 337, showing
n] + 1 [equivalent to] 45 or 83 (mod 127) and they are quadratic nonresidues modulo 127.
n] + 1 [equivalent to] 226, 226 or 212 (mod 239) respectively and they are all quadratic nonresidues modulo 239.
n] + 1 [equivalent to] 11 or 2 (mod 13) respectively and they are quadratic nonresidues modulo 13.
n] + 1 [equivalent to] 3 (mod 29) and 3 is a quadratic nonresidues modulo 29.

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