MathDB

20

Part of 2002 Iran MO (3rd Round)

Problems(1)

Sequence

Source: Iran 2002

4/5/2004
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.
number theory unsolvednumber theory