Fermat's Little Theorem

Understanding Pierre de Fermat’s observation about prime numbers

If p is a prime and a is any integer not divisible by p, then p divides aᵖ⁻¹ - 1.

This property of numbers discovered by Pierre de Fermat in 1640 essentially says the following: Take any prime p and any number a not divisible by that prime. Say, p = 7 and a = 20. By Fermat’s little theorem, we then find that:

Now, we don’t care much about the actual number that results from this calculation. Rather, we care about the fact that without having to do the calculation at all, the theorem tells us that a whole number, an integer, has to result from it. Continue reading


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