If gcd(m, n)= 1 and 1 2 - 2 2 + 3 2 - 4 2 +.... +(2021) 2 - (2022) 2 + (2023) 2 = 1012m 2 n then m 2 - n 2 is equal to
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Let
S = 1 2 - 2 2 + 3 2 - 4 2 +.... +(2021) 2 - (2022) 2 + (2023) 2
S=(1- 2)(1 + 2)+(3 - 4)(3 + 4)+.... +(2021 - 2022)(2021 + 2022)+(2023) 2
S=-[3 + 7+11 + 15+.... +4043]+(2023) 2
The number of terms in the bracket are 
= 1011 
S = 
(6 + 1010 x 4)+(2023) 2
S = -1011 x 2023 + (2023) 2
S = 2023 x 1012
S = 17 2 x 7 x 1012
So,
m = 17, n = 7 and gcd(I7, 7)= 1
Hence, m 2 - n 2 = 17 2 - 7 2 = 240
Hence this is the correct option.
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