https://jaam.aamonline.org.in/ojs/index.php/j <p>The <strong>Journal of the Assam Academy of Mathematics</strong> (JAAM) (Print ISSN 2229-3884) is the flagship journal of the <strong>Assam Academy of Mathematics</strong> and publishes original research articles as well as well-written expository papers on all branches of pure and applied mathematics. <strong>Prof. Anupam Saikia</strong> is the Editor-in-Chief of the journal with several Associate Editors from a diverse mathematical background.</p> <p><strong>Assam Academy of Mathematics</strong><span class="s1"><span class="Apple-converted-space"> </span></span><strong>(অসম গণিত শিক্ষায়তন)</strong>, a non-profit Academic Voluntary organization was established on 18th July, 1986 to promote and popularize mathematics study and research in Assam. Since inception, the Academy has been publishing a quarterly bilingual (Assamese and English) popular magazine on Mathematics named <a href="https://aamonline.org.in/ganit-bikash" target="_blank" rel="noopener"><strong>Ganit Bikash</strong></a>, popular mathematics books in Assamese, etc. It is also organizing Mathematics Olympiad to spot young mathematical talents of the state and academic programmes across the State in fulfillment of the aims and objectives of the organization.</p> Assam Academy of Mathematics en-US Journal of the Assam Academy of Mathematics 2229-3884 <p>Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution (CC-BY) 4.0 License</a> that allows others to share the work with an acknowledgment of the work’s authorship and initial publication in this journal.</p> <p>Provided they are the owners of the copyright to their work, authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of the work (e.g., post it to an institutional repository, in a journal or publish it in a book), with an acknowledgment of its initial publication in this journal.</p> <p>Authors are permitted and encouraged to post their work online (e.g., in institutional repositories, disciplinary repositories, or on their website) prior to and during the submission process.</p> https://jaam.aamonline.org.in/ojs/index.php/j/article/view/58 <p>Some congruences modulo $p^3$ and $p^2$, for a prime $p$ involving binomial coefficients are stated. These appear to be novel.</p> Manjil Saikia Copyright (c) 2023 Author(s) https://creativecommons.org/licenses/by-nc-nd/4.0 2023-12-31 2023-12-31 13 5 7 https://jaam.aamonline.org.in/ojs/index.php/j/article/view/60 <p>For an element $a \in R$, let $\eta(a)=\{e\in R\mid e^2=e\mbox{ and }a-e\in \mbox{nil}(R)\}$. The nil clean index of $R$, denoted by $Nin(R)$, is defined by $Nin(R)=\sup \{\mid \eta(a)\mid: a\in R\}$. In this article we have characterized formal triangular ring $\begin{pmatrix}A &amp; M\\0 &amp; B\end{pmatrix}$ with nil clean index $4$</p> Jayanta Bhattacharyya Dhiren Kumar Basnet Copyright (c) 2023 Author(s) https://creativecommons.org/licenses/by-nc-nd/4.0 2023-12-31 2023-12-31 13 1 4