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Sequence

Source: Iran 2002

April 5, 2004
number theory unsolvednumber theory

Problem Statement

a0=2,a1=1a_{0}=2,a_{1}=1 and for n≥1n\geq 1 we know that : an+1=an+an−1a_{n+1}=a_{n}+a_{n-1} mm is an even number and pp is prime number such that pp divides am−2a_{m}-2. Prove that pp divides am+1−1a_{m+1}-1.
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