Problem #PRU-61140

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

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