MathDB

162

Part of 1972 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 162 All Soviet Union MO 1972 (a^n +1) /(a^m +1) => n/m

Source:

7/3/2019
a) Let a,n,ma,n,m be natural numbers, a>1a > 1. Prove that if (am+1)(a^m + 1) is divisible by (an+1)(a^n + 1) than mm is divisible by nn.
b) Let a,b,n,ma,b,n,m be natural numbers, a>1,aa>1, a and bb are relatively prime. Prove that if (am+bm)(a^m+b^m) is divisible by (an+bn)(a^n+b^n) than mm is divisible by nn.
number theoryrelatively primedivisible