According to Euclid Euler Theorem, a perfect number which is even, can be represented in the form where n is a prime number and is a Mersenne… Read More

# Tag Archives: number-theory

In mathematics, Rosser’s Theorem states that the nth prime number is greater than the product of n and natural logarithm of n for all n… Read More

According to Euler’s four square identity, the product of any two numbers a and b can be expressed as a sum of four squares if… Read More

Given L and R, find a possible non-transitive triplet (a, b, c) such that pair (a, b) is co-prime and pair (b, c) is co-prime… Read More

A cube free number square free number whose none of any divisor is a cubic number (a number which is cube of an integer). Given… Read More

A perfect power is a number that can be expressed as power of another positive integer. Given a number n, find count of numbers from 1… Read More

Nicomachu’s Theorem states that sum of cubes of first n natural numbers is equal to squares of natural number sum.In other wordsOr we can say… Read More

Given two numbers N and M. Find the number of ways in which factorial N can be expressed as a sum of two or more… Read More

The Ramanujan-Nagell equation is an equation between a number (say, x) which is squared and another number (say, z) such that z = . Here,… Read More

Given two positive integer N, M. The task is to check if N and M are friendly pair or not. In number theory, friendly pairs… Read More

According to Fermat’s Last Theorem, no three positive integers a, b, c satisfy the equation, for any integer value of n greater than 2. For n… Read More

Any odd integer greater than 5 can be expressed as a sum of an odd prime (all primes other than 2 are odd) and an… Read More

Find the sum up to n terms of the series: 1.2.3 + 2.3.4 + … + n(n+1)(n+2). In this 1.2.3 represent the first term and… Read More

Prerequisite: Hamiltonian Cycle Given an integer n(>=2), find a permutation of numbers from 1 to n such that the sum of two consecutive numbers of… Read More