



 
Hi Eric, The operator rem $a$ is returning the remainder on division by $a.$ In your example \begin{eqnarray} The operator mod $a$ is one that is used a great deal in number theory, but almost exclusively with $m$ a positive integer. We say that a is congruent to b modulo m if b  a is divisible by m, and denote the relationship by \[a \equiv b \pmod{m}\] Thus \[11 \equiv 1 \pmod{5}\] but so is \[11 \equiv 6 \pmod{5}\] and \[11 \equiv 4 \pmod{5}\] If you are asked to solve $11 \equiv x \pmod{5}$ for $x,$ which one should you return? The convention is to return the value of $x$ that satisfies the congruence and lies between $0$ and $m.$ More explicitly, when $m > 0, x$ satisfies $0 \leq x < m$ and when $m < 0, x$ satisfies $m < x \leq 0.$ I hope this helps,  


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