What 3 positive integers satisfy a^3+b^3=c^3 ?
There is a good discussion of this problem at
http://mathforum.org/library/drmath/view/65003.html
This is, of course, a case involving Fermat's Last Theorem.
To find three positive integers that satisfy the equation a^3+b^3=c^3, we can use the concept known as Euler's sum of powers conjecture. This conjecture states that there are no three positive integers a, b, and c that satisfy the equation a^n+b^n=c^n for any integer n greater than 2.
In the specific case of n=3, which is what we have in the given equation, it is impossible to find three positive integers that satisfy the equation a^3+b^3=c^3.
This concept was famously proven by mathematician Pierre de Fermat in 1637 but the proof is too complex to explain here. It is referred to as Fermat's Last Theorem.
Therefore, there is no solution to the equation a^3+b^3=c^3 for positive integers a, b, and c.