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This document discusses remainders of expressions of the form Aax + Bx modulo some positive integer M. It presents three problems about such expressions from math competitions and generalizes them. It then proves that for any integers A, a, B and positive integer M, there exists a positive integer x such that Aax + Bx is congruent to any integer C modulo M if and only if the greatest common divisor of B and M is 1.

Author

kogleba

Language

EN