| X(p-1) - Y(p-1) = m | X and Y not equal to p, a prime |
| X(p-1) (-1) - Y(p-1) (+1) =m | Subtract and Add a 1 |
| (X(p-1) -1) - (Y(p-1) -1) = m | Associate and factor a (-1) |
| p(t) - p(u) = m | Factor p via Little Fermat Theorem |
| p(t-u) = pk | Substituting m=pk and Factoring p |
| X(p-1) - Y(p-1) = 0 mod(p) | Substituting and applying mod |