6

Part of 2017 Czech And Slovak Olympiad III A

Problems(1)

k =\frac{x^2 - xy + 2y^2}{x + y} has odd no of ordered integer pairs when 7/k

Source: Czech and Slovak Olympiad 2017, National Round, III A p6

Given is a nonzero integer

k

. Prove that equation

k =\frac{x^2 - xy + 2y^2}{x + y}

has an odd number of ordered integer pairs

(x, y)

k

is divisible by seven.

number theorydivisible