Q. 123.6( 5 Votes )

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

Answer :

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

This means 1010 = A^{2}- B^{2}

∵1010 is even number

∴ Either A and B are even numbers or odd numbers

So, A^{2} - B^{2} 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.

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