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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)
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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