Giuga number

A Giuga number is a squarefreeMathworldPlanetmath composite numberMathworldPlanetmath n such that each prime factorMathworldPlanetmath pi|(npi-1). For these numbers it then follows that nBϕ(n)-1modn, (where Bx is a Bernoulli numberDlmfDlmfMathworldPlanetmathPlanetmath).

The first few Giuga numbers are 30, 858, 1722, 66198, 2214408306, 24423128562 (listed in sequence A007850 of Sloane’s OEIS).

All known Giuga numbers are even and have at least three factors. An odd Giuga number would have to have at least twelve factors.

Title Giuga number
Canonical name GiugaNumber
Date of creation 2013-03-22 15:50:22
Last modified on 2013-03-22 15:50:22
Owner Mravinci (12996)
Last modified by Mravinci (12996)
Numerical id 7
Author Mravinci (12996)
Entry type Definition
Classification msc 11D85
Related topic PrimaryPseudoperfectNumber