if m and n are positive integers and m ^ 2 + n ^ 2 = 137 , what is the value of m ^ 3 + n ^ 3 ?
you need to integers which squared are equal 40 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 9 ^ 2 = 81 10 ^ 2 = 100 11 ^ 2 = 121 stop . the integers ca n ' t be greater than 6 or we will score above 137 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 9 ^ 2 = 81 10 ^ 2 = 100 11 ^ 2 = 121 the only pair that matches is 11 ^ 2 + 4 ^ 2 = 137 . so 11 ^ 3 + 4 ^ 3 = 1395 . answer e . )
gcd(137, const_4)