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if 2013 divides $x^{1433} + y^{1433} then divides also x^7 + y^7

Source: 2013 Saudi Arabia Pre-TST 4.2

September 13, 2020
number theorydividesdivisible

Problem Statement

Let x,yx, y be two integers. Prove that if 20132013 divides x1433+y1433x^{1433} + y^{1433} then 20132013 divides x7+y7x^7 + y^7.
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