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Some Extensions on NumbersDOI: 10.4236/apm.2019.911047, PP. 944-958 Keywords: Factorial, Fermat’s Little Theorem, Fermat’s Last Theorem, Euler’s Totient Function, Totient Function of nth Factorial, Totient Function of nth Exponent, Division on Exponents, Prime Bases on Fermat’s Last Theorem, Exponent Parallelogram, Addition Triangle, Difference Triangle, Multiplication Triangle, Division Triangle, Exponent Triangle 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.
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