 If we pair those two absent remainders together, their product will be formula_41 rather than formula_25, whence in this case formula_43.In summary, considering these two cases we have demonstrated that for formula_44 we have formula_45, It remains to substitute formula_46 (which is obviously a square) into this formula to obtain at once Wilson's theorem, Euler's criterion, and (by squaring both sides of Euler's criterion) Fermat's little theorem.Example 1