The difference of the squares of two numbers is equal to the square of 10. Which are these numbers?
If $x$ and $y$ (where $x > y$) are the numbers we are looking for, then the problem requires solving the equation

$$
x^{2}-y^{2}=(x+y)(x-y)=100
$$

It is evident that $x$ and $y$ must have the same parity: either both are even or both are odd. This implies that both $x-y$ and $x+y$ are even numbers.

Accordingly, 100 must be factored into two even numbers; since $x-y < x+y$, the only possibility is

$$
x-y=2 \quad \text{and} \quad x+y=50
$$

From this, we get:

$$
2x=52, \quad x=26 \quad \text{and} \quad y=24
$$

Indeed:

$$
26^{2}-24^{2}=676-576=100
$$

Dezso Szittyai (Mano Wagner Gymnasium IV. grade, Rákospalota.)[^0]


[^0]:    ${ }^{1} x-y=10$ and $x+y=10$ lead to the trivial solution $x=10, y=0$.