Number theory · Divisibility · Linear combinations · Modular arithmetic
Problem 2, 1999
Let \(x\) and \(y\) be integers. Prove that if \(6x + 11y\) is divisible by \(31\), then \(x + 7y\) is divisible by \(31\) as well.
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Serbian Municipal Competition 1999, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source