MathDB
"Nice" numbers

Source: APMC 2006, Problem 4

September 9, 2006
number theory proposednumber theory

Problem Statement

A positive integer dd is called nice iff for all positive integers x,yx,y hold: dd divides (x+y)5−x5−y5(x+y)^{5}-x^{5}-y^{5} iff dd divides (x+y)7−x7−y7(x+y)^{7}-x^{7}-y^{7} . a) Is 29 nice? b) Is 2006 nice? c) Prove that infinitely many nice numbers exist.
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