MathDB

2

Part of 2016 Gulf Math Olympiad

Problems(1)

another number theory problem

Source: GMO 2016

9/28/2017
Let xx be a real number that satisfies x1+x−1=3x^1 + x^{-1} = 3 Prove that xn+x−nx^n + x^{-n} is an positive integer , then prove that the positive integer x31437+x3−1437x^{3^{1437}}+x^{3^{-1437}} is divisible by at least 1439×214371439 \times 2^{1437} positive integers
GMO-Gulf Mathmatical Olympiadnumber theory