Question 1

What is modular arithmetic?

Accepted Answer

Modular arithmetic works with remainders after division. The expression a mod n (read 'a modulo n') is the remainder when a is divided by n. The result is always in the range 0 to n-1. Modular arithmetic underpins clocks, calendars and modern cryptography.

Question 2

What is a modular inverse?

Accepted Answer

The modular inverse of a modulo n is a number x such that (a * x) mod n = 1. An inverse exists only when a and n are coprime, that is gcd(a, n) = 1. This calculator uses the extended Euclidean algorithm to find it.

Question 3

How is modular exponentiation computed?

Accepted Answer

Computing a^b mod n directly would create astronomically large numbers, so we use the fast square-and-multiply algorithm. It processes the exponent bit by bit, squaring and reducing mod n at each step, which is how RSA encryption stays efficient.

Question 4

Can this handle very large numbers?

Accepted Answer

Yes. The calculator uses JavaScript BigInt, so it works with integers of hundreds or thousands of digits. This makes it suitable for cryptography homework and RSA-style computations without losing precision.