Austria 2010

We assume that there are two integers $x,y$ with $$2010=x^2-y^2=(x-y)(x+y).$$ The factors $(x-y)$ and $x+y=(x-y)+2y$ have the same parity.

• If both of them were odd, the product $2010$ would be odd which also gives a contradiction.

• If both of them were even, the product $2010$ would be divisible by $4$ which gives a contradiction.

Therefore, there are no such numbers.