### Representations by certain octonary quadratic forms with coefficients 1, 5, or 25

#### Abstract

It is an important objective to determine the number of representations of a positive integer by certain quadratic forms in number theory. Formulae for $% N(1^{2i},2^{2j},3^{2k},6^{2l};n)$ for the nine octonary quadratic forms appear in the literature, whose coefficients are $1,2,3$ and $6$. Moreover, the formulae for $N(1^{i},3^{j},9^{k};n)$ for several octonary quadratic forms have been given by Alaca. Here, we determine formulae, for $N(1^{i},5^{j},25^{k};n)$ for several octonary quadratic forms.

**How to Cite this Article:**Barış Kendirli, Representations by certain octonary quadratic forms with coefficients 1, 5, or 25, Journal of Mathematical and Computational Science, Vol 8, No 5 (2018), 553-578 Copyright © 2018 Barış Kendirli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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