Little math problems September 2018

09262018, 10:20 PM
(This post was last modified: 09272018 08:35 PM by Albert Chan.)
Post: #15




RE: Little math problems September 2018
Using (2,2) as base, one general solution for square / cube puzzle:
Below equality work for all nonnegative integer n: (2^{6n+1})^{2} + (2^{6n+1})^{2} = 2^{12n+3} = (2^{4n+1})^{3} (2^{6n+1})^{3} + (2^{6n+1})^{3} = 2^{18n+4} = (2^{9n+2})^{2} Edit: For *all* base (a,b), positive integer k, scale up k^{6} will work. So, Valentin big examples (post #7) automatically work, because base = (2,2): 9500208482 = 2 * 41^6 993962581922 = 2 * 89^6 7081411940532321969341507101262893738689268797761826852357921359507223378 = 2 * 1234567890123^6 Looking at above k = 1234567890123, seems Valentin already know this 

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