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14 divides ab if 7a + 8b = 14c + 28d

Source: Austria Beginners' Competition 2012 p1

December 26, 2021
number theorydividesdivisible

Problem Statement

Let a,b,ca, b, c and dd be four integers such that 7a+8b=14c+28d7a + 8b = 14c + 28d. Prove that the product aā‹…ba\cdot b is always divisible by 1414.
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