%0 Journal Article
%T Some Extensions on Numbers
%A Balasubramani Prema Rangasamy
%J Advances in Pure Mathematics
%P 944-958
%@ 2160-0384
%D 2019
%I Scientific Research Publishing
%R 10.4236/apm.2019.911047
%X 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.
%K Factorial
%K Fermat¡¯s Little Theorem
%K Fermat¡¯s Last Theorem
%K Euler¡¯s Totient Function
%K Totient Function of nth Factorial
%K Totient Function of nth Exponent
%K Division on Exponents
%K Prime Bases on Fermat¡¯s Last Theorem
%K Exponent Parallelogram
%K Addition Triangle
%K Difference Triangle
%K Multiplication Triangle
%K Division Triangle
%K Exponent Triangle
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=96739