MathDB

14

Part of 2016 Hanoi Open Mathematics Competitions

Problems(2)

2015a^2+a = 2016b^2+b, \sqrt{a-b} is natural (HOMC 2016 J Q14)

Source:

8/6/2019
Given natural numbers a,ba,b such that 2015a2+a=2016b2+b2015a^2+a = 2016b^2+b. Prove that a−b\sqrt{a-b} is a natural number.
algebraradicalnatural
f(m)=f(2015) f(2016), f (x)=x^2 +px +q (HOMC 2016 S Q14)

Source:

9/8/2019
Let f(x)=x2+px+qf (x) = x^2 + px + q, where p,qp, q are integers. Prove that there is an integer mm such that f(m)=f(2015)⋅f(2016)f (m) = f (2015) \cdot f (2016).
algebrapolynomialtrinomial