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## Elementary Number Theory.

Congruences Pages Jones, Gareth A. Show next xx. Outline of Course Aim: To introduce fundamental topics in elementary number theory. GCD, prime and composite numbers, factorisation of numbers, fundamental theorem of arithmetic 3 lectures Residues, Euler's quotient function, Euler-Fermat theorems, Chinese Remainder theorem.

Method of Fermat descent. Fermat and Lagrange theorems. Prerequisites For details of prerequisites, corequisites, excluded combinations, teaching methods, and assessment details, please see the Faculty Handbook.

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This paper shows that the product of the prime numbers adding and subtracting one is always Simple Prime numbers. This paper develops the divisibility of the so-called Simple Primes numbers 1 to 11 , the discovery of a pattern to infinity, the demonstration of the Inharmonics that are 2,3,5,7 and 11 and the harmony of 1.

The discovery of infinite The discovery of infinite harmony represented in fractal numbers and patterns. This is a family before the prime numbers. The simple prime numbers are known as the rough numbers. Goldbach Conjecture proof. In this paper, I show the proof of Goldbach conjecture.

## Number theory

Since every natural number can be represented using only zeros and ones over base two, we prove a theorem that factors certain numbers immediately and then show that st-space can be used to factor other cases, thus extending the method to Since every natural number can be represented using only zeros and ones over base two, we prove a theorem that factors certain numbers immediately and then show that st-space can be used to factor other cases, thus extending the method to all binary representations. It is without doubt that mathematics, the science of numbers, today owes a huge debt to the outstanding contributions made by Indian mathematicians over many hundreds of years.

- Elementary Number Theory with Programming;
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- Elementary Number Theory | Gareth A. Jones | Springer?
- Between good & evil : polarities of power!

From zero to geometry, Indian mathematicians made some great Frankly speaking, without the Indian numerals, mathematics, as we know it today, would simply not exist. This article is to focus on some of these achievements and to show that mathematics was not only very much rooted in Indian soil but also that ancient Indians had great romance with mathematics.

This paper explicates the Riemann hypothesis and proves its validity. Proof of Cramer's conjecture and Riemann's Hypothesis.

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In this research, a proof of Cramer's conjecture is proposed. The result of the proof is used to prove Riemann hypothesis.

Proof of Cramer's conjecture. An attempt to prove Fermat's Last Theorem Statement.