For any positive integer n, we define Sn=n∑k=12kk2.Prove that there are no polynomials P,Q with real coefficients such that for any positive integer n, we have Sn+1Sn=P(n)Q(n).
Source: 2021 Peru TST D1P3
Tags: number theory, algebra
For any positive integer n, we define Sn=n∑k=12kk2.Prove that there are no polynomials P,Q with real coefficients such that for any positive integer n, we have Sn+1Sn=P(n)Q(n).