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- Steven Gimbel, John Jaroma, James Jospeh Sylvester, John H. Jaroma
- 2003

In 1888, James Joseph Sylvester (1814-1897) published a series of papers that he hoped would pave the way for a general proof of the nonexistence of an odd perfect number (OPN). Seemingly unaware that more than fifty years earlier Benjamin Peirce had proved that an odd perfect number must have at least four distinct prime divisors, Sylvester began his… (More)

- John H. Jaroma, Kamaliya N. Reddy
- The American Mathematical Monthly
- 2007

- Jennifer T. Betcher, John H. Jaroma
- The American Mathematical Monthly
- 2003

A proof of the Lucas–Lehmer test can be difficult to find, for most textbooks that state the result do not prove it. Over the past two decades, there have been some efforts to produce elementary versions of this famous result. However, the two that we acknowledge in this note did so by using either algebraic numbers or group theory. It also appears that in… (More)

Twenty-five years ago, W. M. Snyder extended the notion of a repunit Rn to one in which for some positive integer b, Rn(b) has a b-adic expansion consisting of only ones. He then applied algebraic number theory in order to determine the pairs of integers under which Rn(b) has a prime divisor congruent to 1 modulo n. In this paper, we show how Snyder's… (More)

- John H. Jaroma
- 2004

It is known that with a very small number of exceptions, for a term of a Lehmer sequence {U n (√ R, Q)} to be prime its index must be prime. with the exception that primality may occur if the index is a power of two. Furthermore, given an arbitrary prime p or any positive integer k, there does not exist an explicit means for determining whether U p , V p ,… (More)

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