On a theorem of Zumkeller related to twin primes
Clash Royale CLAN TAG#URR8PPP
up vote
2
down vote
favorite
Let $p_1,p_2$ be a twin prime pair, $phi(n)$ denote Euler's totient function and $sigma(n)$ the sum-of-divisors function. Reinhard Zumkeller proved in 2002 that
$$
phi(p_2) = sigma(p_1).
$$
However I cannot find Zumkeller's paper proving this fact. Can anyone kindly point me to a link where I can read his Theorem?
reference-request prime-numbers divisor-sum prime-twins
add a comment |Â
up vote
2
down vote
favorite
Let $p_1,p_2$ be a twin prime pair, $phi(n)$ denote Euler's totient function and $sigma(n)$ the sum-of-divisors function. Reinhard Zumkeller proved in 2002 that
$$
phi(p_2) = sigma(p_1).
$$
However I cannot find Zumkeller's paper proving this fact. Can anyone kindly point me to a link where I can read his Theorem?
reference-request prime-numbers divisor-sum prime-twins
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Let $p_1,p_2$ be a twin prime pair, $phi(n)$ denote Euler's totient function and $sigma(n)$ the sum-of-divisors function. Reinhard Zumkeller proved in 2002 that
$$
phi(p_2) = sigma(p_1).
$$
However I cannot find Zumkeller's paper proving this fact. Can anyone kindly point me to a link where I can read his Theorem?
reference-request prime-numbers divisor-sum prime-twins
Let $p_1,p_2$ be a twin prime pair, $phi(n)$ denote Euler's totient function and $sigma(n)$ the sum-of-divisors function. Reinhard Zumkeller proved in 2002 that
$$
phi(p_2) = sigma(p_1).
$$
However I cannot find Zumkeller's paper proving this fact. Can anyone kindly point me to a link where I can read his Theorem?
reference-request prime-numbers divisor-sum prime-twins
reference-request prime-numbers divisor-sum prime-twins
edited Sep 9 at 11:44
joriki
169k10181337
169k10181337
asked Sep 9 at 10:30
PierreTheFermented
1,3421927
1,3421927
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
4
down vote
accepted
There's not much to prove, certainly not enough for a paper. $phi(p_2)=p_2-1$, as for any prime, and $sigma(p_1)=p_1+1$, as for any prime; since they're twin primes, $p_2-1=p_1+1$.
1
Oh, indeed :) Thanks!
â PierreTheFermented
Sep 9 at 12:33
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
There's not much to prove, certainly not enough for a paper. $phi(p_2)=p_2-1$, as for any prime, and $sigma(p_1)=p_1+1$, as for any prime; since they're twin primes, $p_2-1=p_1+1$.
1
Oh, indeed :) Thanks!
â PierreTheFermented
Sep 9 at 12:33
add a comment |Â
up vote
4
down vote
accepted
There's not much to prove, certainly not enough for a paper. $phi(p_2)=p_2-1$, as for any prime, and $sigma(p_1)=p_1+1$, as for any prime; since they're twin primes, $p_2-1=p_1+1$.
1
Oh, indeed :) Thanks!
â PierreTheFermented
Sep 9 at 12:33
add a comment |Â
up vote
4
down vote
accepted
up vote
4
down vote
accepted
There's not much to prove, certainly not enough for a paper. $phi(p_2)=p_2-1$, as for any prime, and $sigma(p_1)=p_1+1$, as for any prime; since they're twin primes, $p_2-1=p_1+1$.
There's not much to prove, certainly not enough for a paper. $phi(p_2)=p_2-1$, as for any prime, and $sigma(p_1)=p_1+1$, as for any prime; since they're twin primes, $p_2-1=p_1+1$.
answered Sep 9 at 11:45
joriki
169k10181337
169k10181337
1
Oh, indeed :) Thanks!
â PierreTheFermented
Sep 9 at 12:33
add a comment |Â
1
Oh, indeed :) Thanks!
â PierreTheFermented
Sep 9 at 12:33
1
1
Oh, indeed :) Thanks!
â PierreTheFermented
Sep 9 at 12:33
Oh, indeed :) Thanks!
â PierreTheFermented
Sep 9 at 12:33
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2910650%2fon-a-theorem-of-zumkeller-related-to-twin-primes%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password