Discrete Calculator

A simple yet powerful calculator with functions for number theory and combinatorics.

The functions of Number Theory are:

1) gcd(a,b): the Greatest Common Divisor of a and b.
2) lcm(a,b): the Least Common Multiple of a and b.
3) pmod(a,b): the remainder of the division of a by b.
4) pmod(a,b,c): the remainder of the division of (a^b) by c.
5) smod(a,b,c): one solution of the equation aX ≡ b mod c.
6) φ(n): Euler's totient function, returns the number of positive integers up to a given integer n that are relatively prime to n.
7) prime factors: type an expression and press the "prime factors" button, to receive the answer as a product of prime factors, if possible.
8) sol diof lin: for a Diophantine equation of the type ax+by=c, type (a,b,c) and press the "sol diof lin" button, to receive the solution of the respective equation.

The functions of Combinatorics are:

1) P(n): = the number of permutations of n distinct elements, i.e., n!.
2) P(n,b1,b2,...,bk): the number of permutations of n elements with b1, b2, ..., bk as repeted elements.
3) A(n,p): the number of p-permutations of a set of n distinct objects, i.e., n*(n-1)*(n-2)*...*(n-p+1).
4) C(n,p): the binomial coefficient n over p, i.e., n!/(p!*(n-p)!).
5) Cr(n,p): the number C(n+p-1, p), i.e., the number of p-combinations of n elements, allowing repetition of these elements.
6) D(n): the number of derangements of n distinct elements.
7) D(n,p): the number of permutations with p fixed points.
8) K(n,p): the number C(n-p+1,p), 1º Kaplanky's Lemma.
9) K(n,p,r): the number C(n-(p-1)*r,p), Generalization of the 1º Kaplanky's Lemma.
10) Kc(n,p): the number (n/(n-p))*C(n-p,p), 2º Kaplanky's Lemma.
11) Kc(n,p,r): the number (n/(n-p*r))*C(n-p*r, p), Generalization of the 2º Kaplanky's Lemma.
12) rand(n,p): a random number between n and p.

Recent changes:
Add left parentheses autocomplete, when adding a right parentheses and there aren't enough left parentheses for the expression to make sense.