[Primes Home][Home]
If we have the form of \(x^2 = y \pmod p\), we must find a value of \(x\) which results in a value of \(y \pmod p\). It is actually a difficult problem to solve. If a solution exists, the value of \(y\) is a quadratic residue (mod p). In modular arithmetic this operation is equivalent to a square root of a number (and where \(x\) is the modular square root of a modulo \(p\)). In the following we will try and solve for the value of \(x\). In this case we will create a modulus (\(N\)), and which is the product of two
prime numbers (\(p\) and \(q\)):