Smallest quadratic nonresidue

From Number
Jump to: navigation, search

Definition

Let be a prime number. The smallest quadratic nonresidue modulo is the smallest positive integer such that the congruence class of modulo is not a square; in other words, is the smallest quadratic nonresidue modulo .

The smallest quadratic nonresidue modulo a prime is always a prime.

Facts and conjectures

  • Extended Riemann hypothesis: This states that the smallest quadratic nonresidue modulo is less than . This is a conjecture, and has not been proved.

Facts