Question

Can 1010 be written as a difference of two perfect squares? [Hint: How many times 2 occurs as a factor of 1010?]

Answer 1

Suppose

Since 1010 is even, both x and y are either even or odd.

Therefore, is divisible by 4.

However, 1010 is not divisible by 4 as 10 is not divisible by 4.

Hence, 1010 cannot be written as the difference of two perfect squares.