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Question
Find the least positive value of x such that 5x ≡ 4 (mod 6)
Solution
To find the least value of x such that
5x ≡ 4 (mod 6)
5x – 4 = 6M for some integer n.
5x = 6n + 4
x = `(6"n" + 4)/5`
When we put 1, 6, 11, … as n values in x = `(6"n" + 4)/5` which is divisible by 5.
When n = 1, x = `10/5` = 2
When n = 6, x = `(36 + 4)/5 = 40/5` = 8 and so on.
∴ The solution are 2, 8, 14 …..
∴ Least value is 2.
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