# Tag Archives: number-theory

Nesbitt’s inequality is one of the simplest inequalities in mathematics. According to the statement of the inequality, for any 3 given real numbers they satisfy… Read More
Lagrange’s Four Square Theorem states that every natural number can be written as sum of squares of four non negative integers. For eg. Similarly Similarly for any … Read More
Hardy Ramanujam theorem states that the number of prime factors of n will approximately be log(log(n)) for most natural numbers nExamples :   5192 has 2… Read More
Given an integer ‘n’, print the first ‘n’ terms of the Moser-de Bruijn Sequence. The Moser-de Bruijn sequence is the sequence obtained by adding up… Read More
Brahmagupta Fibonacci identity states that the product of two numbers each of which is a sum of 2 squares can be represented as sum of… Read More
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
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