IMO 1982 LL GBR33

A sequence (un) of integers is defined for n \geq0 by u0 = 0,

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IMO 1982 LL GBR33

Origin: GBR

Problem

A sequence (un) of integers is defined for n \geq0 by u0 = 0, u1 = 1, and un −2un−1 + (1 −c)un−2 = 0 (n \geq2), where c is a fixed integer independent of n. Find the least value of c for which both of the following statements are true: (i) If p is a prime less than or equal to P, then p divides up. (ii) If p is a prime greater than P, then p does not divide up.