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Some Extensions on Numbers
Former Student of Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India
- 1 Former Student of Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India
Advances in Pure Mathematics·Volume 09 (2019)·Pages 944–958·Published 4 November 2019·DOI10.4236/apm.2019.911047
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Abstract
My previous work dealt finding numbers which relatively prime to factorial value of certain number, high exponents and also find the way for finding mod values on certain number’s exponents. Firstly, I retreat my previous works about Euler’s phi function and some works on Fermat’s little theorem. Next, I construct exponent parallelogram to find coherence numbers of Euler’s phi functioned numbers and apply to Fermat’s little theorem. Then, I test the primality of prime numbers on Pascal’s triangle and explore new ways to construct Pascal’s triangle. Finally, I find the factorial value for certain number by using exponent triangle.
KeywordsFactorialFermat’s Little TheoremFermat’s Last TheoremEuler’s Totient FunctionTotient Function of nth FactorialTotient Function of nth ExponentDivision on ExponentsPrime Bases on Fermat’s Last TheoremExponent ParallelogramAddition TriangleDifference TriangleMultiplication TriangleDivision TriangleExponent Triangle
- Pomerance, C. and Crandall, R. (2005) Prime Numbers: A Computational Perspective. 2nd Edition, Springer, New York.
- Chaudhuri, S. (2014) Fermat’s Little Theorem-CS 2800: Discrete Structures.
- Balasubramani, P.R. (2019) Fermat’s Theorem One Extension. Mathematical Sciences International Journal, 8, 6-10.