<div>Modular arithmetic is used in discrete math to find remainders. The definition states, if <span class="ltx_Math" contenteditable="false" data-equation="a">\(a\)</span>&nbsp;and&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="b">\(b\)</span>&nbsp;are both integers and&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="m>0">\(m&gt;0\)</span>&nbsp; then&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="a">\(a\)</span>&nbsp;is congruent to <span class="ltx_Math" contenteditable="false" data-equation="b">\(b\)</span>&nbsp;(mod <span class="ltx_Math" contenteditable="false" data-equation="m">\(m\)</span>) if <span class="ltx_Math" contenteditable="false" data-equation="m">\(m\)</span>&nbsp;divides <span class="ltx_Math" contenteditable="false" data-equation="a-b">\(a-b\)</span>.&nbsp;The notion of modular arithmetic deals with the remainders that are found in Euclidean division. The actions of trying to find the remainder is also known as modulo operation or (mod <span class="ltx_Math" contenteditable="false" data-equation="n">\(n\)</span>) where <span class="ltx_Math" contenteditable="false" data-equation="n">\(n\)</span>&nbsp; is a an integer. For instance, the division of <span class="ltx_Math" contenteditable="false" data-equation="8">\(8\)</span>&nbsp;by <span class="ltx_Math" contenteditable="false" data-equation="3">\(3\)</span>&nbsp;can also be written as&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="8">\(8\)</span>&nbsp;(mod <span class="ltx_Math" contenteditable="false" data-equation="3">\(3\)</span>) and we can find the remainder to equal <span class="ltx_Math" contenteditable="false" data-equation="2">\(2\)</span> thus, <span class="ltx_Math" contenteditable="false" data-equation="8">\(8\)</span>&nbsp;(mod <span class="ltx_Math" contenteditable="false" data-equation="3">\(3\)</span>) <span class="ltx_Math" contenteditable="false" data-equation="=2">\(=2\)</span>. <br></div>