Giuga number

A Giuga number is a composite number n such that for each of its distinct prime factors p_i we have ${\displaystyle p_{i}|({n \over p_{i}}-1)}$, or equivalently such that for each of its distinct prime factors p_i we have ${\displaystyle p_{i}^{2}|(n-p_{i})}$.

The Giuga numbers are named after the mathematician Giuseppe Giuga, and relate to his conjecture on primality.

Alternative definition for a Giuga number due to Takashi Agoh is: a composite number n is a Giuga number if and only if the congruence

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