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47 divides 3^x - 2^y iff 23 divides 4x + y.

Source: 2013 Saudi Arabia Pre-TST 1.2

September 13, 2020
number theorydividesdivisible

Problem Statement

Let x,yx, y be two non-negative integers. Prove that 4747 divides 3xāˆ’2y3^x - 2^y if and only if 2323 divides 4x+y4x + y.
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