MathDB

2

Part of 2015 Dutch IMO TST

Problems(2)

Polynomials

Source:

5/4/2018
Determine all polynomials P(x) with real coefficients such that [(x + 1)P(x − 1) − (x − 1)P(x)] is a constant polynomial.
Polynomialsalgebrapolynomial
system in N*: a_1 + 2a_2 +... + na_n = 6n, 1/a_1+2/a_2+... +n/a_n=2+1/n

Source: Dutch IMO TST 2015 day 2 p2

8/30/2019
Determine all positive integers nn for which there exist positive integers a1,a2,...,ana_1,a_2, ..., a_n
with a1+2a2+3a3+...+nan=6na_1 + 2a_2 + 3a_3 +... + na_n = 6n and 1a1+2a2+3a3+...+nan=2+1n\frac{1}{a_1}+\frac{2}{a_2}+\frac{3}{a_3}+ ... +\frac{n}{a_n}= 2 + \frac1n
system of equationsDiophantine Equationsdiophantinenumber theory