Little math problems September 2018
09-27-2018, 11:45 PM
Post: #17
 Albert Chan Senior Member Posts: 2,516 Joined: Jul 2018
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 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
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 Messages In This Thread Little math problems September 2018 - pier4r - 09-20-2018, 11:21 AM RE: Little math problems September 2018 - Thomas Klemm - 09-20-2018, 12:54 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 01:03 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 02:37 PM RE: Little math problems September 2018 - Albert Chan - 09-25-2018, 02:46 AM RE: Little math problems September 2018 - ijabbott - 09-20-2018, 04:55 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 05:22 PM RE: Little math problems September 2018 - Valentin Albillo - 09-24-2018, 12:53 AM RE: Little math problems September 2018 - Albert Chan - 09-24-2018, 12:18 PM RE: Little math problems September 2018 - Valentin Albillo - 09-25-2018, 12:48 AM RE: Little math problems September 2018 - Albert Chan - 09-28-2018, 04:51 PM RE: Little math problems September 2018 - pier4r - 09-25-2018, 10:56 AM RE: Little math problems September 2018 - Valentin Albillo - 09-25-2018, 04:09 PM RE: Little math problems September 2018 - pier4r - 09-26-2018, 03:55 PM RE: Little math problems September 2018 - Valentin Albillo - 09-26-2018, 08:13 PM RE: Little math problems September 2018 - Albert Chan - 09-26-2018, 10:20 PM RE: Little math problems September 2018 - pier4r - 09-28-2018, 01:36 PM RE: Little math problems September 2018 - pier4r - 09-27-2018, 10:42 PM RE: Little math problems September 2018 - Albert Chan - 09-27-2018 11:45 PM

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