Problem #PRU-61140

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)
 13–15  3.0

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) \((x^2 + x + 1)^3\)?