Does there exist any positive integral solution of the equation given below?
16(X³+Y³) + 12(X²+Y²) + 3(X+Y) = 2,138,156,388
(In reply to
re: Full solution by Kenny M)
Modulo 7 partitions the infinity of integers into a finite number, 7, groups such that what works (or does not work) for a sample element of an equivalence class works (or does not work) for all the others in that equivalence class.
0...6 are in different equivalence classes modulo 7. I could equally well have used 1...7. or any other set of 7 integers from different equivalence classes e.g. 1, 9, 17,...
Having tested the 42 combinations of these, none of which give 4 mod 7, I have effectively tested all the integers and found no solutions in integers, including the positive integers.
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Posted by goFish
on 2005-12-29 13:42:06 |
re(2): Full solution
