MathDB

2011 PUMaC Number Theory A7

Source:

September 24, 2019

number theory

Problem Statement

Let

\{g_i\}_{i=0}^{\infty}

be a sequence of positive integers such that

g_0=g_1=1

and the following recursions hold for every positive integer

n

: \begin{align*} g_{2n+1} &= g_{2n-1}^2+g_{2n-2}^2 \\ g_{2n} &= 2g_{2n-1}g_{2n-2}-g_{2n-2}^2 \end{align*} Compute the remainder when

g_{2011}

is divided by

216