A theorem that tests if a quadratic residue is a square.
Modular arithmetic: The arithmetic of remainders when dividing integers by a fixed integer modulus.
Fermat's little theorem: A fundamental theorem in number theory stating that if p is prime and a is an integer not divisible by p, then a^(p-1) is congruent to 1 modulo p.
Euler's totient function: A function that gives the number of positive integers less than or equal to n that are relatively prime to n.
Modular multiplicative inverse: An integer x such that ax is congruent to 1 modulo m.
Jacobi symbol: A generalization of the Legendre symbol that allows for testing quadratic residues and non-residues modulo any odd integer.
Quadratic reciprocity law: A fundamental theorem in number theory stating that for any two odd primes p and q, the Legendre symbol of p modulo q equals the Legendre symbol of q modulo p, up to a sign.
Primitive roots: A number a such that every residue modulo p can be expressed as a power of a modulo p, where p is a prime.
Tonelli-Shanks algorithm: An algorithm for finding the square root of a quadratic residue modulo a prime p.
Binary quadratic forms: Expressions of the form Ax^2 + Bxy + Cy^2, where A, B, C are integers and x, y are variables.
Pell's equation: An equation of the form x^2 - Dy^2 = 1, where D is a non-square integer.
Continued fractions: A method for approximating real numbers as a sequence of rational numbers with convergents.
Modular forms: Complex analytic functions that satisfy certain transformation properties under the modular group SL(2,Z).