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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:Theorem. Let \( n \in \mathbb{N} \) and let \( a \in \mathbb{Z} \). If \( a = nq + r \) and \( 0 \leq r < n \) for some integers \( q \) and \( r \), then \( a \equiv \) _______________.
Corollary. If \( n \in \mathbb{N} \), then each integer is congruent, modulo \( n \), to precisely one of the integers \( 0, 1, \ldots, \). That is, for each integer \( a \), there exists a unique integer \( r \) such that \( a \equiv \)
-------------------- and \( 0 \leq r < \) _________.
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