MathDB

2.1

Part of 2024 Belarus Team Selection Test

Problems(1)

A sequence of reals which produce perfect squares

Source: Belarus TST 2024

7/17/2024
A sequence {yi}\{y_i\} is given, where y0=−14,y1=0y_0=-\frac{1}{4},y_1=0. For every positive integer nn the following equality holds: yn−1+yn+1=4yn+1y_{n-1}+y_{n+1}=4y_n+1 Prove that for every positive integer nn the number 2y2n+322y_{2n}+\frac{3}{2} a) is a positive integer b) is a square of a positive integer D. Zmiaikou
Sequencealgebranumber theory