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Modular Arithmetic

205+ posts

Collatz Conjecture: Fun Facts and More

Last Updated: 23 July 2025

Collatz Conjecture or 3n + 1 Conjecture or Ulam Conjecture, is the problem in mathematics for almost a decade. It is proposed in 1937 by Lothar Collatz. Although extensive...read more

article_image

Modular Arithmetic

CSES Solutions - Exponentiation II

Last Updated: 23 July 2025

Your task is to efficiently calculate values a^(b^c) modulo 109+7.Note that in this task we assume that 00 = 1.Examples:Input: N = 2, queries[][] = {{3, 7, 1}, {2, 3, 2}}O...read more

Modular Arithmetic

Binary Exponentiation

Modular Arithmetic for Competitive Programming

Last Updated: 23 July 2025

In mathematics, modular arithmetic refers to the arithmetic of integers that wraps around when a certain value is reached, called the modulus. This becomes particularly cr...read more

Modular Arithmetic

Geeks Premier League 2023

Binary Exponentiation for Competitive Programming

Last Updated: 18 June 2026

In competitive programming, we often need to calculate large powers like xy, where y can be as large as 109 or more. Using a simple loop takes O(y) time, which is ineffici...read more

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Competitive Programming

Modular Arithmetic

Binary Exponentiation

BPSK - Binary Phase Shift Keying

Last Updated: 23 July 2025

Binary Phase Shift Keying (BPSK) is a widely used modulation technique in digital communication systems for transmitting binary data over a communication channel. It is kn...read more

Modular Arithmetic

General Electric

Electronics Engineering

Minimizing numbers through subtraction operations

Last Updated: 07 November 2023

Given two numbers given as P and Q, the task is to make both numbers equal in the minimum number of operations, where you are allowed to perform the below operations any ...read more

Modular Arithmetic

Count ways choosing K balls from any given A boxes

Last Updated: 23 July 2025

Given integers A and K, there are A boxes the first box contains K balls, the Second box contains K + 1 balls, the Third Box contains K + 3 balls so on till the A'th box c...read more

Dynamic Programming

Technical Scripter

Technical Scripter 2022

Modular Arithmetic

Count number of ways in which following people can be arranged

Last Updated: 23 July 2025

Given integers X and Y representing X girls and Y boys, the task is to count the number of ways arranging X girls and Y boys such that girls always stay together and two b...read more

Technical Scripter

Technical Scripter 2022

Modular Arithmetic

Minimize Array size by replacing adjacent integers by their Modulo

Last Updated: 23 July 2025

Given an array arr[] of positive integers of size N, the task is to find the minimum possible size of the array that can be obtained by replacing any two adjacent positive...read more

Technical Scripter

Technical Scripter 2022

Modular Arithmetic

frequency-counting

Maximum multiple of a number with all digits same

Last Updated: 07 March 2024

Given two positive integers X and Y (1 ? Y ? 105), find the maximum positive multiple (say M) of X such that M is less than 10Y and all the digits in the decimal represent...read more

Modular Arithmetic

Minimize distinct elements in Array after replacing arr[i] with arr[i] modulo X

Last Updated: 14 October 2022

Given an array arr[] of size N, the task is to minimize the number of distinct elements in the array after performing the following operation once:Choose an integer X and ...read more

Modular Arithmetic

12-Hour Clock Multiplication

Last Updated: 29 June 2026

Given two positive integers a and b, find the product of the two numbers on a 12-hour clock rather than a number line.Note: Assume the Clock starts from 0 hours to 11 hour...read more

Computer Science Fundamentals

Modular Arithmetic

Count of Pairs such that modulo of product of one with their XOR and X is 1

Last Updated: 10 January 2023

Given two arrays A[] and B[] of length N and M respectively and a prime number X, the task is to find the number of ordered pair of indices (i, j) that satisfies the follo...read more

Modular Arithmetic

Find minimum and maximum number of terms to divide N as sum of 4 or 6

Last Updated: 02 August 2022

Given an integer N, the task is to find the minimum and the maximum number of terms required to divide N as the sum of 4 or 6.Examples:Input: N = 3Output: NOT POSSIBLEExpl...read more

Modular Arithmetic

Compute nCr % p | Set 4 (Chinese Remainder theorem with Lucas Theorem)

Last Updated: 23 July 2025

Given three numbers n, r and p, the task is to compute the value of nCr % p.Note: p is a square-free number and the largest prime factor of p ≤ 50.Examples:Input: n = 10, ...read more

Modular Arithmetic

Permutation and Combination

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