MathDB

Problem 1

Part of 2017 Pan African

Problems(1)

Problem 1 sequence of integer is square

Source: PAMO 2017 Problem 1

7/5/2017
We consider the real sequence (xn)(x_n) defined by x0=0,x1=1x_0=0, x_1=1 and xn+2=3xn+1−2xnx_{n+2}=3x_{n+1}-2x_n for n=0,1,...n=0,1,... We define the sequence (yn)(y_n) by yn=xn2+2n+2y_n=x_n^2+2^{n+2} for every non negative integer nn. Prove that for every n>0n>0, yny_n is the square of an odd integer
algebraPAMO