MathDB

Let

x_{1}

and

x_{2}

be relatively prime positive integers. For

n \ge 2

, define

x_{n+1}=x_{n}x_{n-1}+1

.[*] Prove that for every

i>1

, there exists

j>i

such that

{x_{i}}^{i}

divides

{x_{j}}^{j}

. [*] Is it true that

x_{1}

must divide

{x_{j}}^{j}

for some

j>1

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