Fundamental Theorem Of Arithmetic Research Articles

The board stretcher: A model to introduce factors, primes, composites, and multiplication by a fraction

Most children are aware that some numbers are even and the rest are odd, but they know little else about our number system. The “board-stretcher” model provides a means to discovering the idea of factors and obtaining a feeling for prime and composite numbers. It portrays the inverse relation between multiplication and division and, as a finale, it can be used to introduce the concept of multiplication by a fraction. This model suggests the notion that the sum of the prime factors of a number (except for four) is always less than the product of the factors. The Fundamental Theorem of Arithmetic (or Unique Factorization Theorem) is understood by youngsters when they see that every composite number can be expressed as a product of prime factors that is unique except for the order of the factors.

Mathematics, the Man-Made Universe. An Introduction to the Spirit of Mathematics.

Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topics. Each subject illustrates a significant idea and lends itself easily to experiments and problems. Useful appendices offer an overview of the basic ideas of arithmetic, the rudiments of algebra, suggestions on teaching mathematics, and much more, including answers and comments for selected exercises.

Two Theorems on Mosaics

The concept of a mosaic was recently introduced by A. A. Mullin (1). By the fundamental theorem of arithmetic, every integer n > 1 can be uniquely expressed in the formwhere the pi are primes satisfying p1 < p2 < . . . < pr. We then express any exponents aj which are greater than unity in the same manner, and continue in this way until the process terminates. The resulting planar configuration of primes is called the mosaic of n.

A Proof of the Fundamental Theorem of Arithmetic

A Proof of the Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic

XVIII.—The Elementary Proof of the Prime Number Theorem

SynopsisThe author presents a modification of the recently discovered “elementary” proof of the Prime Number Theorem. Nothing is assumed from the theory of numbers except the Fundamental Theorem of Arithmetic. In the second part of the proof the elements of the integral calculus are used to make clearer the basic ideas on which this part depends.

2160. The fundamental theorem of arithmetic

2160. The fundamental theorem of arithmetic