Fermat’s Last Theorem: What is it?

What exactly did Fermat’s Last Theorem say?  I think many of you are familiar with the Pythagorean Theorem.  That one basically says that you can find a missing side on a right triangle so long as you know the other two sides by using the formula

In working with right triangles, there are several cases where the solutions for a, b, and c are all positive integers (not decimals).  For instance, you can have a = 3, b = 4, and c = 5.  Another example is a = 5, b = 12, and c = 13.  Well, what if the exponent were not 2 but something higher?  Fermat’s theorem says that there are no solutions consisting of entirely positive integers.  It took mathematicians many years to prove this, but Andrew Wiles showed it to be true!


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