Linked from

The 9 pages that link to Euler's criterion, each with the reason it gives.

• Quadratic reciprocityRelated: It connects residue status to a computable power modulo the prime.

• Primality testRelated: Its residue test underlies the Solovay–Strassen test.

• Disquisitiones ArithmeticaeRelated: The criterion supplies a computational test for quadratic residuosity in the book’s framework.

• Legendre symbolRelated: It computes the symbol by modular exponentiation.

• Quadratic residueRelated: It determines quadratic-residue status without listing every square.

• Jacobi symbolRelated: Its Jacobi-symbol analogue underlies the congruence checked by Solovay–Strassen.

• Fermat's theorem on sums of two squaresRelated: It quickly shows that −1 is a quadratic residue precisely for primes congruent to 1 modulo 4.

• Solovay–Strassen primality testRelated: The test generalizes this prime-only identity by replacing the Legendre symbol with the Jacobi symbol.

• Proth's theoremRelated: The test's exponent is half the candidate number minus one.