Number Theory Solver

This app performs 5 fundamental calculations in number theory. These form a basis for many algorithms in cryptography and computer security. They are:

1. Determine if number is prime, or find the smallest prime factor if it is not prime. This can be used repeatedly to find all the prime factors of a number.

2. Find the gcd(m,n) (greatest common divisor) and lcm (least common multiple) of two integers, i.e. the largest integer that divides both numbers.

3. Compute a number mod n, (modular arithmetic), or a number raised to a power mod n, i.e. modular exponentiation a^b mod n. For example 2^50 mod 15.

4. Compute the modular inverse of a number, i.e. solve a*x = 1 mod n, for integer x, given a and n.

5. Find integer solutions x, y to Diophantine equations, i.e. equations of the form ax + by = c, where a, b, c are all integers.

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