Little math problems September 2018

[Albert Chan]

Hi, pier4r

I think my math is right ...

Second formula is to check sum of cubes = a perfect square
Since both terms are the same, binary exponent = 1 + 3 * (6n + 1) = 18 n + 4
Sum of cubes binary exponent is even, thus perfect square.

You can also think of 2⁶ⁿ⁺¹ = 2 * (2ⁿ)⁶, so k = 2ⁿ

If (a, b) is a solution, sum of squares of (k⁶ a, k⁶ b) = cube * k¹² , also a cube
Similarly, sum of cubes of (k⁶ a, k⁶ b) = square * k¹⁸, still a square.

Actually, k can be any integers, not just 2ⁿ