MathDB

217

Part of 1975 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 217 All Soviet Union MO 1975 sequence of sum of digits of P(n)

Source:

7/5/2019
Given a polynomial P(x)P(x) with
a) natural coefficients; b) integer coefficients;
Let us denote with ana_n the sum of the digits of P(n)P(n) value. Prove that there is a number encountered in the sequence a1,a2,...,an,...a_1, a_2, ... , a_n, ... infinite times.
number theorySequencepolynomialsum of digits