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Question
Find the least positive value of x such that 78 + x ≡ 3 (mod 5)
Solution
To find the least value of x such that
78 + x ≡ 3 (mod 5)
⇒ 78 + x – 3 = 5n for some integer n.
75 + x = 5n
75 + x is a multiple of 5.
75 + 5 = 80.
80 is a multiple of 5.
Therefore, the least value of x must be 5.
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