Little math problems September 2018

09272018, 11:45 PM
Post: #17




RE: Little math problems September 2018
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 2^{6n+1} = 2 * (2^{n})^{6}, so k = 2^{n} If (a, b) is a solution, sum of squares of (k^{6} a, k^{6} b) = cube * k^{12} , also a cube Similarly, sum of cubes of (k^{6} a, k^{6} b) = square * k^{18}, still a square. Actually, k can be any integers, not just 2^{n} 

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