![]() The fundamental theorem of arithmetic states that any integer greater than 1 can be written as a product of prime numbers in a unique way (up to the ordering of prime factors in the product). Fundamental Theorem of Arithmetic and the Division AlgorithmĪs the name rightly says, this theorem lies at the heart of all the concepts in number theory. But being the building blocks of arithmetic, these axioms are worth knowing.ġ. The fifth axiom is also popularly known as "principal of mathematical induction"īeing extremely basic, we would rarely need them directly, unless we want to prove every theorem in arithmetic from the first principles. (v) If a set contains the number 0 and it also contains the successor of every number in S, then S contains every natural number. (iv) Different natural numbers have different successors (iii) 0 is not the successor of any natural number (ii) Every natural number has a successor, which is also a natural number The entire formalization of arithmetic is based on five fundamental axioms, called Peano axioms, which define properties of natural numbers. External references (mostly from Wikipedia and Wolfram) have been provided at many places for further details. Rather, this writeup is intended to act as a reference. ![]() It is neither an introductory tutorial, nor any specific algorithms are discussed here. This writeup discusses few most important concepts in number theory that every programmer should ideally know.
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