If _ r=1 ²⁵ ( r r⁴+r²+1 )= p q , where p and q are positive integers such that gcd (p, q)=1 , then p+q is equal to _ _ _ _ 。

Step-by-step solution

S = r (r^2 + r + 1)(r^2 - r + 1) = 1 2 _ r=1 ²⁵ ( 1 r^2 - r + 1 - 1 r^2 + r + 1 ) = 1 2 [ ( 1 1 - 1 3 ) + ( 1 3 - 1 7 ) + + ( 1 601 - 1 651 ) ] = 1 2 [ 1 1 - 1 651 ] = 1 2 [ 650 651 ] = 325 651 p q = 325 651 p + q = 976