MathDB

3

Part of 2020 China Second Round Olympiad

Problems(1)

A new problem about linear recursive sequence

Source: 2020 China Second Round (A) P3

9/13/2020
Let a1=1,a_1=1, a2=2,a_2=2, an=2an−1+an−2,a_n=2a_{n-1}+a_{n-2}, n=3,4,⋯ .n=3,4,\cdots. Prove that for any integer n≥5,n\geq5, ana_n has at least one prime factor p,p, such that p≡1(mod4).p\equiv 1\pmod{4}.
number theoryChinarecurrence relationlinear recurrence