Many of us are familiar with the Pythagorean Theorem. This theorem has many proofs.
The Pythagorean Triples (a,b,c) represent the lengths of the two legs and hypotenuse of right triangles and satisfy the Pythagorean Theorem equation
\(a^2 + b^2 = c^2\)
We can find infinitely many triples. For example, multiply the triplet (3,4,5) by any positive integer and it also satisfies Pythagorean's Theorem
Fermat’s Last Theorem states that there are no positive integers that satisfy the equation with higher degree than 2. That is, for every triple (a,b,c), the following inequalities are always true.
\(a^3 + b^3 ≠ c^3\)
\(a^4 + b^4 ≠ c^4\)
\(a^5 + b^5 ≠ c^5\)
. . .
\(a^n + b^n ≠ c^n\)
In general, it says that there are no positive integers (a,b,c) that satisfy the equation \(a^n + b^n = c^n\), for any integer n greater than 2.
This math problem was proposed by Pierre de Fermat in 1637, and after more than 300 years and many incorrect proofs published, Andrew Wiles finally solved the enigma in 1995. It took him 8 years to solve the problem!