IMO 1969 LL GBR28

Let us define u0 = 0, u1 = 1 and for n \geq0, un+2 = aun+1+bun,

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IMO 1969 LL GBR28

Origin: GBR

Problem

Let us define u0 = 0, u1 = 1 and for n \geq0, un+2 = aun+1+bun, a and b being positive integers. Express un as a polynomial in a and b. Prove the result. Given that b is prime, prove that b divides a(ub −1).