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Find the integer \(n, 0 \le n \le 11\), such that

                                       \(n \equiv 10389 \pmod{12}.\)

 Nov 12, 2020
 #1
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Divide 10389 by 12.  n is the remainder.

 Nov 12, 2020
 #2
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Hello Alan: My "Chinese Remainder Theorem + Modular Multiplicative Inverse" computer code gives the solution as: n =12x + 9, where x =0, 1, 2, 3......etc. Since the value of "n" falls between 0 and 11, according to his/her question, then the smallest n = 9

 Nov 12, 2020

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