Category: Mathematics

A simple recursive method to generate a numeric palindrome from any number is to reverse its digits and add it to the original. If the sum is not a palindrome (which means, it is not the same number from left to right and right to left), repeat this procedure.

The king has many words. For each given word, he needs to find out the number of palindrome anagrams of the string. As the number of anagrams can be large, the king needs the number of anagrams % (10^9+ 7).

In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

On the day of the party, the Chef was over-seeing all the food arrangements as well, ensuring that every item was in its designated position. The host was satisfied with everything except the cupcakes. He noticed they were arranged neatly in the shape of a rectangle. He asks the Chef to make it as square-like as possible.

You are given an integer, N. Write a program to determine if N is an element of the Fibonacci sequence.
The first few elements of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13….

You are given an infinite 2d grid with the bottom left cell referenced as (1,1). All the cells contain a value of zero initially. Let’s play a game?
The game consists of N steps wherein each step you are given two integers a and b.

Matrix multiplication can be performed in O(logn) by using matrix exponentiation. It is one of the most used techniques