MathDB
a_n is always a perfect square.

Source: 2000 China Second Round Olympiad P2

August 13, 2019
number theorySequence

Problem Statement

Define the sequence a1,a2,…a_1, a_2, \ldots and b1,b2,…b_1, b_2, \ldots as a0=1,a1=4,a2=49a_0=1,a_1=4,a_2=49 and for n≥0n \geq 0 {an+1=7an+6bn−3,bn+1=8an+7bn−4. \begin{cases} a_{n+1}=7a_n+6b_n-3, \\ b_{n+1}=8a_n+7b_n-4. \end{cases} Prove that for any non-negative integer n,n, ana_n is a perfect square.
Back to ProblemsView on AoPS