Is it 2015 or 2050?
If x 2 0 5 0 − a 2 0 5 0 + y 2 0 5 0 − b 2 0 5 0 + z 2 0 5 0 − c 2 0 5 0 = 4 6 5 8 9 3
If above equation is true for some integers ( x , y , z , a , b , c ) and the pair of solutions be ( x 1 , y 1 , z 1 , a 1 , b 1 , c 1 ) ,...., ( x n , y n , z n , a n , b n , c n ) . Find the value of
i = 1 ∑ n x i + y i + z i + a i + b i + c i
The answer is 0.
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Two Line Solution:-
If ( x , y , z , a , b , c ) be the solution then ( − x , − y , − z , − a , − b , − c ) will also be the solution. Therefore our answer will be 0 .