MathDB

Let

P(x)=x^{2016}+2x^{2015}+...+2017,Q(x)=1399x^{1398}+...+2x+1

. Prove that there are strictly increasing sequances

a_i,b_i, i=1,...

of positive integers such that

gcd(a_i,a_{i+1})=1

for each

i

. Moreover, for each even

i

P(b_i) \nmid a_i, Q(b_i) | a_i

and for each odd

i

P(b_i)|a_i,Q(b_i) \nmid a_i

Proposed by Shayan Talaei

Problem Statement