MathDB

4

Part of 2019 Nigeria Senior MO Round 2

Problems(1)

Polynomial gcd

Source: Nigeria senior mathematics Olympiad round 2 problem 4.

9/8/2019
Let h(t)h(t) and f(t)f(t) be polynomials such that h(t)=t2h(t)=t^2 and fn(t)=h(h(h(h(h...h(t))))))−1f_n(t)=h(h(h(h(h...h(t))))))-1 where h(t)h(t) occurs nn times. Prove that fn(t)f_n(t) is a factor of fN(t)f_N(t) whenever nn is a factor of NN
algebranumber theorygreatest common divisor