Problem #PRU-61140

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

Problem

For what values of \(n\) does the polynomial \((x+1)^n - x^n - 1\) divide by:

a) \(x^2 + x + 1\); b) \((x^2 + x + 1)^2\); c) \((x^2 + x + 1)^3\)?