20220411, 14:49  #12  
Apr 2020
857 Posts 
Quote:
The real answer is "yes". But you'll have to figure out for yourself why that is. Last fiddled with by charybdis on 20220411 at 14:51 Reason: oops 

20220411, 15:32  #13  
Feb 2017
Nowhere
2^{2}×3×499 Posts 
Quote:
There are two types of solutions: those in which A + B and A^2  A*B + B^2 are each 3 times a perfect square (e.g. 1^3 + 2^3 = 3^2) , and those with each a perfect square (e.g. 56^3 + 65^3 = 671^2). I leave it as an exercise to work out formulas for each case. 

20220412, 04:40  #14 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Does there exist a positive integer N, such that if the sum of the three exponents is >=N (and none of the three exponents is 1, and at most one of the three exponents is 2), then there exist only finitely many solutions other than 2^3+1^n=3^2? If so, find the smallest such positive integer N
(I also think that 2^3+1^n=3^2 will be the only solution if N is enough large) Last fiddled with by sweety439 on 20220412 at 04:42 
20220412, 04:56  #15  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Quote:


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