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Solve the congruence: 19x + 7 congreunce 27 (mod 18).
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19x + 7 = 27 (mod 18) 1x + 7 = 9 (mod 18) 1x = 9-7 (mod 18) 1x = 2 (mod 18) x = 2 (mod 18)
How did you get from step one to two
19 = 1 (mod 18) 27 = 9 (mod 18)
19 = 1 (mod 18) because 19/18 = 1 remainder 1 ------------------------------------------------------- 27 = 9 (mod 18) because 27/18 = 1 remainder 9
so that's how 19x + 7 = 27 (mod 18) turned into 1x + 7 = 9 (mod 18)
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