#### Presentation Title

Repunits: Natural Numbers In Which Every Digit Is A One

#### Mentor

Vincent Ferlini

#### Location

David F. Putnam Science Center - 102

#### Abstract

A repunit (a contraction of “repeating units”) is a natural number in which every digit is a one. This talk will discuss two interesting properties that are related to repunits and prime numbers. The first property is the fact that every prime number, other than two and five, is a factor of at least one repunit. The second is that each repunit is divisible by a prime that does not divide any smaller repunit. This talk will conclude with some statements of unsolved questions involving repunits and some possible ways of approaching them.

Repunits: Natural Numbers In Which Every Digit Is A One

David F. Putnam Science Center - 102

A repunit (a contraction of “repeating units”) is a natural number in which every digit is a one. This talk will discuss two interesting properties that are related to repunits and prime numbers. The first property is the fact that every prime number, other than two and five, is a factor of at least one repunit. The second is that each repunit is divisible by a prime that does not divide any smaller repunit. This talk will conclude with some statements of unsolved questions involving repunits and some possible ways of approaching them.