If a polynomial equation Q has a root for this operation applied to the equation Q with respect to a prime p, then there will exist a unique root for Q for this operation applied to a power of p by Hensel's lifting lemma.
If a polynomial equation Q has a root for this operation applied to the equation Q with respect to a prime p, then there will exist a unique root for Q for this operation applied to a power of p by Hensel's lifting lemma. An odd prime p is expressible as the sum of two squares if and only if a form of this operation applied to p yields one according to one of many results called Fermat's Theorem. For two numbers a and p, a raised to p minus 1 divided by two applied to this operation of p gives the (*) Legendre symbol, giving conditions for when the golden theorem can be satisfied. Both linear and quadratic residue classes are defined using this operation. Wilson's theorem states that a number n is prime if and only if n minus one factorial is congruent to negative one of this function of n. A percent sign is used to represent, for 10 points, what operation that gives the remainder after division?
If a polynomial equation Q has a root for this operation applied to the equation Q with respect to a prime p, then there will exist a unique root for Q for this operation applied to a power of p by Hensel's lifting lemma.
modulo [accept modulus; prompt on remainder] 