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#1 2007-09-27 14:06:44

Mort
Guest

Linear congruence

This problem was confusing me, so if anyone could explain it step by step, it would be greatly appreciated!

Find all incongruent solutions to the following linear congruence:

21x ≡ 14 (mod 91)

#2 2007-09-27 21:31:42

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Linear congruence

You can divide through by 7.

3x ≡ 2 (mod 13)

By inspection, x = 5 is one solution. Since gcd(3,13) = 1, all the other solutions are therefore multiples of 13 apart from one another. Hence the solution set is {5+13k: k integer}.

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