SOLUTION: find all possible pairs (a,b) of integers such that a^3=5b^3

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Question 900982: find all possible pairs (a,b) of integers such that a^3=5b^3
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
(0,0) is a solution

Assume, for contradiction, that there are other solutions:

If (a,b) is a solution then (-a,-b) ia also a solution.
So we only need consider that a and b are positive integers.

a%5E3=5b%5E3

a%5E3%2Fb%5E3=5

%28a%2Fb%29%5E3=5

a%2Fb is a rational number which is the cube root of 5.

But the cube root of 5 is irrational.

Thus we have reached a contradiction.

Thus (0,0) is the only solution.

Edwin