N^3+N^3=N^3

Question

I can't solve this question.Please help me. I have an example of it
N^2+N^2=N^2
3^2+4^2=5^2
9+16=25
25=25
both become equal.And don't use 0
Please help me.

Answer 1

There is no solution.

 

This is a problem that dates back to Euler and Fermat.

 

There is actually a cool story to it. Fermat famously scribbled in the margin of a book that there are no integer solutions to xⁿ+yⁿ=zⁿ when n>2. He said he had an elegant proof of this, but there was no room in the margin so he would write it elsewhere...

 

If he wrote it anywhere, it was never found and it took hundreds of years to finally prove his assertion (google Fermat's Last Theorem)