The following opertions/syntax are supported:
×
| Operation | Examples | Explanation |
|---|---|---|
+, -, *, / |
3*45 |
Arithmetic, observes common sense operator precedence |
a \times b, a \cdot b |
3\times 45 |
Multiplication, same as a*b |
\frac{a}{b} |
\frac{5}{12}, \frac23 |
$\frac{a}{b}$ |
x^y |
3^100 |
$x^y$ |
n!, n!! |
16! |
The factorial and double factorial of $n$ |
\binom{n}{k} |
\binom{15}{3}, \binom84 |
The binomial coefficient $\binom{n}{k}$ |
gcd(a,b), lcm(a,b) |
gcd(12,15), lcm(3,5,8) |
The greatest common divisor, and the least common multiple. Supports arbitrary number of arguments. |
isprime(n) |
isprime(2^16+1) |
Whether $n$ is a prime number |
nextprime(n) |
nextprime(2^16+1) |
The smallest prime number $>n$ |
nextprimes(n, k) |
nextprimes(11, 5) |
The $k$ smallest prime numbers $>n$ |
primelist(a, b) |
primelist(100, 200) |
All prime number $p$ such that $a \leq p \leq n$ |
factor(n) |
primelist(100, 200) |
The prime factorization of $n$ |
adic(p, n) |
adic(3, 10^6-1) |
The p-adic number $v_p(n)$, where $p$ must be a prime |
totient(n) |
totient(24) |
The Euler's totient function $\varphi(n)$ |
floor(x), ceil(x) |
floor(35/8) |
The floor $\lfloor x \rfloor$ and ceil $\lceil x \rceil$ |
a mod b or a \pmod{b} |
2^100 mod 3 |
$a \pmod{b}$. Note that
|
jacobi(a,b) or kronecker(a,b) |
jacobi(21, 5) |
Both mean the Kronecker symbol $\begin{pmatrix} a \cr \hdashline b \cr \end{pmatrix}$. Note when $b$ is an odd integer, Kronecker symbol is same as Jacobi symbol. |
Session history:
Input math expression below (use "clear" to clear session history):
[1]: