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Simultaneous Values Of The Totient Function, Nelson Carella Aug 2023

Simultaneous Values Of The Totient Function, Nelson Carella

Publications and Research

A pair of integers $n$ and $n+k$ is a simultaneous solution of an arithmetic function $f:\mathbb{N}\longrightarrow \mathbb{R}$ if $f(n)=f(n+k)$, where $k\ne0$ is a fixed integer. This article shows that the totient function has infinitely many simultaneous solutions. In particular, $\varphi(n)=\varphi(n+2)$ infinitely often as $n\to\infty$.


Contributors Aug 2023

Contributors

The Mythic Circle

No abstract provided.


Mythic Circle #45 Aug 2023

Mythic Circle #45

The Mythic Circle

No abstract provided.


The Marble Princess, Lawrence Buentello Aug 2023

The Marble Princess, Lawrence Buentello

The Mythic Circle

No abstract provided.


Ode To Joy Or The Way Of Eloquence, David Sparenberg Aug 2023

Ode To Joy Or The Way Of Eloquence, David Sparenberg

The Mythic Circle

No abstract provided.


Black Dragon Ship, David Sparenberg Aug 2023

Black Dragon Ship, David Sparenberg

The Mythic Circle

No abstract provided.


A Great Strength Of Time, Kevan Kenneth Bowkett Aug 2023

A Great Strength Of Time, Kevan Kenneth Bowkett

The Mythic Circle

No abstract provided.


Black Dragon Keep, Lee Clark Zumpe Aug 2023

Black Dragon Keep, Lee Clark Zumpe

The Mythic Circle

No abstract provided.


The Book Of The Dragon, Sandy Feinstein Aug 2023

The Book Of The Dragon, Sandy Feinstein

The Mythic Circle

No abstract provided.


A Circle Of Dragons, A. J. Prufrock Aug 2023

A Circle Of Dragons, A. J. Prufrock

The Mythic Circle

No abstract provided.


A Forefather Of Fantasy, Andoni Cossio Aug 2023

A Forefather Of Fantasy, Andoni Cossio

The Mythic Circle

No abstract provided.


Silver Lining, Kevan Kenneth Bowkett Aug 2023

Silver Lining, Kevan Kenneth Bowkett

The Mythic Circle

No abstract provided.


I Have Guests, Russ Bickerstaff Aug 2023

I Have Guests, Russ Bickerstaff

The Mythic Circle

No abstract provided.


Editors' Introductions Aug 2023

Editors' Introductions

The Mythic Circle

No abstract provided.


Walking, Llewellyn Issel Aug 2023

Walking, Llewellyn Issel

The Mythic Circle

No abstract provided.


The Gathering, David Sparenberg Aug 2023

The Gathering, David Sparenberg

The Mythic Circle

No abstract provided.


All Of The Notes / Some Of The Reasons Why, Holly Day Aug 2023

All Of The Notes / Some Of The Reasons Why, Holly Day

The Mythic Circle

No abstract provided.


The Lark Mirror, Angelisa Fontaine-Wood Aug 2023

The Lark Mirror, Angelisa Fontaine-Wood

The Mythic Circle

No abstract provided.


Originating Dragons, Sandy Feinstein Aug 2023

Originating Dragons, Sandy Feinstein

The Mythic Circle

No abstract provided.


Dragon Fall, Lawrence Buentello Aug 2023

Dragon Fall, Lawrence Buentello

The Mythic Circle

No abstract provided.


The Death Of Wyac, Geoffrey Reiter Aug 2023

The Death Of Wyac, Geoffrey Reiter

The Mythic Circle

No abstract provided.


The Symphony Of Rosaline, J. Brice Odom Aug 2023

The Symphony Of Rosaline, J. Brice Odom

The Mythic Circle

No abstract provided.


The Penultimate Dodo, Geoffrey Reiter Aug 2023

The Penultimate Dodo, Geoffrey Reiter

The Mythic Circle

No abstract provided.


West Of The Moon, Elizabeth Scott Tervo Aug 2023

West Of The Moon, Elizabeth Scott Tervo

The Mythic Circle

No abstract provided.


Under A Horned Red Moon, Kevan Kenneth Bowkett Aug 2023

Under A Horned Red Moon, Kevan Kenneth Bowkett

The Mythic Circle

No abstract provided.


Gweir The Warrior, Joe Christopher Aug 2023

Gweir The Warrior, Joe Christopher

The Mythic Circle

No abstract provided.


Demon And Dog-Man, S. Dorman Aug 2023

Demon And Dog-Man, S. Dorman

The Mythic Circle

No abstract provided.


She-We-Eucatastrophe, David Sparenberg Aug 2023

She-We-Eucatastrophe, David Sparenberg

The Mythic Circle

No abstract provided.


Phillip "Phil" Ricks Aug 2023

Phillip "Phil" Ricks

African American Funeral Programs

No abstract provided.


Deacon Freddie Walter Grant Sr. Aug 2023

Deacon Freddie Walter Grant Sr.

African American Funeral Programs

Funeral Program for Deacon Freddie Walter Grant Sr. on Aug. 5, 2023 at The Original First African Baptist Church