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2010 Distinct solution to a linear congruence
Donald Adams, Vadim Ponomarenko
Involve 3(3): 341-344 (2010). DOI: 10.2140/involve.2010.3.341

Abstract

Given n,k and a1,a2,,akn, we give conditions for the equation a1x1+a2x2++akxk=1 in n to admit solutions with all the xi distinct.

A sufficient condition is that kϕ(n) and ai be invertible in n for all i.

If n>2 is prime, the following conditions together are necessary and sufficient: kn, each ai is nonzero, and either k<n or not all of the ai are equal.

Citation

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Donald Adams. Vadim Ponomarenko. "Distinct solution to a linear congruence." Involve 3 (3) 341 - 344, 2010. https://doi.org/10.2140/involve.2010.3.341

Information

Received: 7 July 2010; Revised: 29 September 2010; Accepted: 29 September 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1222.11005
MathSciNet: MR2739524
Digital Object Identifier: 10.2140/involve.2010.3.341

Subjects:
Primary: 11B50, 11D79

Rights: Copyright © 2010 Mathematical Sciences Publishers

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