MathDB

10

Part of 1987 Romania Team Selection Test

Problems(1)

divizibility

Source: L. Panaitopol,Romania, TST 1987

8/10/2005
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
modular arithmeticinductionfunctionalgebrapolynomialnumber theory proposednumber theory