Question
Find the smallest positive integer n such that 6n + 5 is
divisible by 7.Solution
ATQ,
6n + 5 ≡ 0 mod7 → 6n ≡ 2 → n ≡ 2×6⁻¹ mod7 → 6⁻¹ ≡ 6 (since 6×6 ≡ 1 mod7) → n ≡ 12 ≡ 5 mod7 → n = 5.
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