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 = 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.


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