have solutions in nonzero integers a,b,c ? The answer is “NO.” Sometime around 1637, Pierre de Fermat showed that there is no solution for exponent 4. During the eighteenth and nineteenth centuries, Carl Friedrich Gauss and Leonhard Euler showed that there is no solution for exponent 3 and Lejeune Dirichlet and Adrien Legendre dealt with the exponent 5. The general problem of showing that the equation