https://math.codidact.com/categories/41/tags/6946.rssNew Posts Tagged 'modular-arithmetic' - MathematicsMathematics - Codidact2023-05-29T10:38:46Zhttps://math.codidact.com/posts/288168Closed-form expression for sum of Modulo Arithmetic Progressiontheabbieâ€https://math.codidact.com/users/537872023-05-28T16:41:05Z2023-05-29T10:38:46Z<p>Is there any closed-form expression or at least an efficient way to calculate this sum?</p>
$$ \sum_{i=1}^{N} (a \cdot i) \bmod{M} $$<p>we can assume $N$, $a$, and $M$ are large enough such tha...https://math.codidact.com/posts/287063Show that $\forall n \in \mathbb{Z}^{+}$, $25^n \equiv 25 \bmod{100}$.Carefree Explorerâ€https://math.codidact.com/users/568512022-09-24T14:21:59Z2022-10-03T08:24:13Z<blockquote>
<p>Show that $\forall n \in \mathbb{Z}^{+}$, $25^n \equiv 25 \bmod{100}$.</p>
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<p>This was a simple observation I made when playing around and I came up with the follow...