How do I break down the math symbols in this equation
$begingroup$
$$frac{n}{phi(n)}=frac{n}{nprod_{p|n}left(1-frac{1}{p}right)}=frac{1}{prod_{p|n}left(1-frac{1}{p}right)}$$
How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?
notation
edited 1 hour ago
Robert Howard
2,0381927
asked 1 hour ago
Po Chen LiuPo Chen Liu
1148
$endgroup$
add a comment |
$begingroup$
$$frac{n}{phi(n)}=frac{n}{nprod_{p|n}left(1-frac{1}{p}right)}=frac{1}{prod_{p|n}left(1-frac{1}{p}right)}$$
How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?
notation
edited 1 hour ago
Robert Howard
2,0381927
asked 1 hour ago
Po Chen LiuPo Chen Liu
1148
$endgroup$
1
$begingroup$
The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
$endgroup$
– Minus One-Twelfth
1 hour ago
$begingroup$
For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
$endgroup$
– Mark S.
1 hour ago
add a comment |
$begingroup$
$$frac{n}{phi(n)}=frac{n}{nprod_{p|n}left(1-frac{1}{p}right)}=frac{1}{prod_{p|n}left(1-frac{1}{p}right)}$$
How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?
notation
edited 1 hour ago
Robert Howard
2,0381927
asked 1 hour ago
Po Chen LiuPo Chen Liu
1148
$endgroup$
$$frac{n}{phi(n)}=frac{n}{nprod_{p|n}left(1-frac{1}{p}right)}=frac{1}{prod_{p|n}left(1-frac{1}{p}right)}$$
How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?
notation
notation
edited 1 hour ago
Robert Howard
2,0381927
asked 1 hour ago
Po Chen LiuPo Chen Liu
1148
edited 1 hour ago
Robert Howard
2,0381927
asked 1 hour ago
Po Chen LiuPo Chen Liu
1148
edited 1 hour ago
Robert Howard
2,0381927
edited 1 hour ago
Robert Howard
2,0381927
edited 1 hour ago
Robert Howard
2,0381927
2,0381927
asked 1 hour ago
Po Chen LiuPo Chen Liu
1148
asked 1 hour ago
Po Chen LiuPo Chen Liu
1148
asked 1 hour ago
Po Chen LiuPo Chen Liu
1148
1148
1
$begingroup$
The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
$endgroup$
– Minus One-Twelfth
1 hour ago
$begingroup$
For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
$endgroup$
– Mark S.
1 hour ago
add a comment |
1
$begingroup$
The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
$endgroup$
– Minus One-Twelfth
1 hour ago
$begingroup$
For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
$endgroup$
– Mark S.
1 hour ago
1
1
$begingroup$
The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
$endgroup$
– Minus One-Twelfth
1 hour ago
$begingroup$
The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
$endgroup$
– Minus One-Twelfth
1 hour ago
$begingroup$
For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
$endgroup$
– Mark S.
1 hour ago
$begingroup$
For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
$endgroup$
– Mark S.
1 hour ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.
As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$
answered 1 hour ago
John DoeJohn Doe
11.2k11238
$endgroup$
add a comment |
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1 Answer
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$begingroup$
The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.
As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$
answered 1 hour ago
John DoeJohn Doe
11.2k11238
$endgroup$
add a comment |
$begingroup$
The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.
As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$
answered 1 hour ago
John DoeJohn Doe
11.2k11238
$endgroup$
add a comment |
$begingroup$
The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.
As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$
answered 1 hour ago
John DoeJohn Doe
11.2k11238
$endgroup$
The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.
As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$
answered 1 hour ago
John DoeJohn Doe
11.2k11238
answered 1 hour ago
John DoeJohn Doe
11.2k11238
answered 1 hour ago
John DoeJohn Doe
11.2k11238
answered 1 hour ago
John DoeJohn Doe
11.2k11238
11.2k11238
add a comment |
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$begingroup$
The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
$endgroup$
– Minus One-Twelfth
1 hour ago
$begingroup$
For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
$endgroup$
– Mark S.
1 hour ago