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michellen2020
13.07.2019 •
Mathematics
Solve the congruence 169x 25 (mod 330)
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Ответ:
First solve the congruence
. Euclid's algorithm shows
330 = 25 * 13 + 5
13 = 2 * 5 + 3
5 = 1 * 3 + 2
3 = 1 * 2 + 1
=> 1 = 127 * 13 - 5 * 330
=> 127 * 13 = 1 mod 330
so that
is the inverse of 13 modulo 330. Then in the original congruence, multiplying both sides by 127 twice gives
Then any integer of the form
is a solution to the congruence, where
is any integer.
Ответ: