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1. (Mathematics) Fermat's Little Theorem: Let "a" be a natural number (i.e. a number that is at least 1 and does not contain fractional parts), and let "p" be a (positive) prime number, where the greatest common divisor of "a" and "p" (i.e. gcd (a, p)) is 1, then, Fermat's Little Theorem states that a ^ (p - 1) is equivalent to 1 (mod p) read: "a raised to the power of (p - 1) divided by p has a remainder of 1". Therefore, a^p is equivalent to a (mod p) This is often used in RSA and other Public Key Infrastructure. 2. (Mathematics) Fermat's Last Theorem: Let "x", "y" and "z" be non-zero integers, and let "n" be a natural number (see above) greater than 2, then, there will not exist an equation x^n + y^n = z^n read: "(x to the power of n) plus (y to the power of n) equals (z to the power of n)" for any "x", "y", "z" and "n" combinations.
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