Pythagoras's Theorem states that if a and b are the shorter lengths of a right angled triangle, the length of the longer side, c, is such that a^2 + b^2 = c^2.
There are plenty of Pythagorian triples. That is, non-zero whole numbers (integers) a and b such that c is itself a whole number. Examples include (3, 4, 5) and (5, 12, 13).
My question is that if instead of squaring, we raise the number to a higher power, are there any more triples. Eg. is there a non-trivial solution to a^3 + b^3 = c^3 or a^4 + b^4 = c^4? One example would be fine.
Otherwise, does anyone have a short proof in the unlikely situation that there is no solution?
2006-11-29
11:16:26
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3 answers
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asked by
Morosoph
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in
Mathematics