Modular exponentiation is a exponentiation performed over modulus. It is used in many cryptographic algorithms.

Modular exponentiation accepts three input integers, say x, y and n and computes according to the formula below,

(x ^ y) mod n

Native Approaches

A naive approach to compute modular exponentiation is to compute the exponentiation first and [...]

Fibonacci series is a number sequence of 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 44, … It can be expressed by the formula below,

Fibonacci series grows almost as fast as the power of 2. Fn ~= 2^(0.694n).

Computation of Fibonacci Numbers
The naive approach to compute [...]

This is a post for a set of problems that deals with millions of integers. Part 1 deals with how to generate millions of integers.

This is normally used as a program to generate inputs for testing subsequent problems. We’ll look at two problems with a slight difference.

1. Allow user to input [...]

Side Note: This is first written on Oct 17 2007.

Euclid’s algorithm is used to find the greatest common divisor for two positive integers, let’s say m and n. It’s the first algorithm introduced in Knuth’s classic book, <<The Art of Computer Programming >> . The following text are retrieved from the book,