“The story starts with Pierre de Fermat, one of the all-time great mathematicians, who claimed he could prove that the equation (a^n+ b^n = c^n) has no whole number solutions when n is greater than 2. There are some near misses (e.g., 6^3 + 8^3 = 9^3 – 1), but no numbers that make the equation balance properly.”

I think it has to do with Pythagorean’s Theorem where for any right triangle the sum of the square of each leg = the square of the hypotenuse, which put another way is to say two congruent right triangles joined will make a square and when the opposing diagonal is drawn four equally sized equilateral triangles result. Each equilateral triangle is necessarily 1/4 the area of the square. Taking any two of the equilateral triangles reconstructs the equivalent area of the larger right triangle. Now we have six equal sides proving the Pythagorean theorem. There is no equivalent theorem for n > 2.