MathDB

1

Part of 2020 New Zealand MO

Problems(2)

max n such that 50!/2^n is an integer

Source: New Zealand MO 2020 Round 1 p1

9/20/2021
What is the maximum integer nn such that 50!2n\frac{50!}{2^n} is an integer?
number theoryInteger
if P(r) = 0 then Q(r^2) = 0, P(x) = x^3 - 2x + 1, Q(x) = x^3 - 4x^2 + 4x - 1

Source: 2020 New Zealand MO Round 2 p1 NZMO

9/22/2021
Let P(x)=x3−2x+1P(x) = x^3 - 2x + 1 and let Q(x)=x3−4x2+4x−1Q(x) = x^3 - 4x^2 + 4x - 1. Show that if P(r)=0P(r) = 0 then Q(r2)=0Q(r^2) = 0.
algebrapolynomial