Vitaliy V. answered • 01/21/23
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Math and Statistics Tutor with 30+ years of experience
15x = 9 (mod 27) means that 15x = 27k + 9. Divide the equality by 3: 5x = 9k + 3, or 5x = 3 (mod 9).
It is easy to find that from x = 0, 1, 2, ..., 8 only x=6 satisfies the equation: 5*6 = 30 = 9*3 + 3.
So, the solutions are 6 + 9k.
If we need only solutions that are less than 27, they are 6, 15, and 24.