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2011 is not a divisor of ab -cd if a+b+c+d = 2011

Source: 2011 Saudi Arabia Pre-TST November 4.4

January 1, 2022
number theorydivisordivides

Problem Statement

Let a,b,c,da, b, c, d be positive integers such that a+b+c+d=2011a+b+c+d = 2011. Prove that 20112011 is not a divisor of abāˆ’cdab - cd.
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