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

We are required to find two perfect squares such that 1010 can be written as a difference of two perfect squares.

This means 1010 = A²- B²

∵1010 is even number

∴ Either A and B are even numbers or odd numbers

So, A² - B² is divisible by 4 but 1010 is not divisible by 4 because 1010 = 10 × 101 = 2 × 5 × 101

Hence, 1010 cannot be expressed as a difference of two perfect squares.