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divizibility

Source: L. Panaitopol,Romania, TST 1987

August 10, 2005
modular arithmeticinductionfunctionalgebrapolynomialnumber theory proposednumber theory

Problem Statement

Let a,b,ca,b,c be integer numbers such that (a+b+c)∣(a2+b2+c2)(a+b+c) \mid (a^{2}+b^{2}+c^{2}). Show that there exist infinitely many positive integers nn such that (a+b+c)∣(an+bn+cn)(a+b+c) \mid (a^{n}+b^{n}+c^{n}). Laurentiu Panaitopol
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