Pace P. Nielsen

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20042025

most citedOdd Perfect Numbers Have At Least Nine Distinct Prime Factors

17 citations · 56 across the 8 of their papers we have counts for

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math.NT2022

Prime factors of $Φ_{3} (x)$ of the same form

Cody S. Hansen, Pace P. Nielsen

We parameterize solutions to the equality $Φ_{3} (x) = Φ_{3} (a_{1}) Φ_{3} (a_{2}) \dots Φ_{3} (a_{n})$ when each $Φ_{3} (a_{i})$ is prime. Our focus is on the special cases when $n = 2, 3, 4$ , as this analysis…

math.NT2017★ 11 cited

Covering systems with restricted divisibility

Robert D. Hough, Pace P. Nielsen

We prove that every distinct covering system has a modulus divisible by either 2 or 3.

math.NT2006★ 17 cited

Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

Pace P. Nielsen

An odd perfect number, N, is shown to have at least nine distinct prime factors. If 3 does not divide N, then N must have at least twelve distinct prime divisors. The proof ultimat…

Prime factors of Φ3​(x) of the same form

Covering systems with restricted divisibility

Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

Prime factors of $Φ_{3} (x)$ of the same form