Odd Perfect Numbers: A Divisor Related to the Euler′s Factor Original Research Article

Let n = παM2 be an odd perfect number; πα, with π prime, (π, M) = 1 and π ≡ α ≡ 1 (mod 4), is the Euler′s factor of n. It is shown that: if α + 2 is prime or pseudoprime in base π and (α + 2, π − 1) = 1, then M2 ≡ 0 (mod α + 2).