euler-totient

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Count of integers up to N which are non divisors and non coprime with N

Last Updated: 02 December 2021

Given an integer N, the task is to find the count of all possible integers less than N satisfying the following properties:The number is not coprime with N i.e their GCD i ...read more

Sum of GCD of all numbers upto N with N itself

Last Updated: 23 November 2022

Given an integer N, the task is to find the sum of Greatest Common Divisors of all numbers up to N with N itself.Examples:Input: N = 12Output: 40Explanation:GCD of [1, 12] ...read more

Find (1^n + 2^n + 3^n + 4^n) mod 5 | Set 2

Last Updated: 09 June 2022

Given a very large number N. The task is to find (1n + 2n + 3n + 4n) mod 5.Examples:Input: N = 4Output: 4(1 + 16 + 81 + 256) % 5 = 354 % 5 = 4Input: N = 782346293782633287 ...read more

Mathematical

Competitive Programming

euler-totient

DSA

Find the number of primitive roots modulo prime

Last Updated: 29 June 2022

Given a prime[Tex]p[/Tex]. The task is to count all the primitive roots of[Tex]p[/Tex].A primitive root is an integer x (1 = x p) such that none of the integers x - 1, x2 ...read more

Mathematical

Competitive Programming

Queries to count the number of unordered co-prime pairs from 1 to N

Last Updated: 01 September 2022

Given a number N. The task is to find the number of unordered coprime pairs of integers from 1 to N. There can be multiple queries.Examples:Input: 3Output: 4(1, 1), (1, 2) ...read more

Compute power of power k times % m

Last Updated: 24 May 2022

Given x, k and m. Compute (xxxx...k)%m, x is in power k times. Given x is always prime and m is greater than x.Examples:Input : 2 3 3Output : 1Explanation : ((2 ^ 2) ^ 2) ...read more

Minimum insertions to make a Co-prime array

Last Updated: 10 October 2022

Given an array of N elements, find the minimum number of insertions to convert the given array into a co-prime array. Print the resultant array also.Co-prime Array : An ar ...read more

Optimized Euler Totient Function for Multiple Evaluations

Last Updated: 17 September 2022

Euler Totient Function (ETF) Φ(n) for an input n is count of numbers in {1, 2, 3, …, n} that are relatively prime to n, i.e., the numbers whose GCD (Greatest Common Diviso ...read more

Number Theory | Generators of finite cyclic group under addition

Last Updated: 20 February 2023

Given a number n, find all generators of cyclic additive group under modulo n. Generator of a set {0, 1, ... n-1} is an element x such that x is smaller than n, and using ...read more

Primitive root of a prime number n modulo n

Last Updated: 08 March 2023

Given a prime number n, the task is to find its primitive root under modulo n. The primitive root of a prime number n is an integer r between[1, n-1] such that the values ...read more

Euler's Totient function for all numbers smaller than or equal to n

Last Updated: 17 September 2022

Euler's Totient function Φ(n) for an input n is the count of numbers in {1, 2, 3, ..., n} that are relatively prime to n, i.e., the numbers whose GCD (Greatest Common Divi...read more

Euler's Totient Function

Last Updated: 25 January 2023

Euler's Totient function Φ (n) for an input n is the count of numbers in {1, 2, 3, ..., n-1} that are relatively prime to n, i.e., the numbers whose GCD (Greatest Common D...read more

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