One dividing a positive integer n by 9, we get 7 as remainder. What will be the remainder if (3n – 1) is divided by 9?

Using Euclid’s division lemma –

n = 9(q) + 7, where q is the quotient when divided by 9.


3n = 9(3q) + 21 { multiply by 3 on both sides }


3n = 9(3q) + 18 + 3


3n = 9(3q + 2) + 3 (I)


Also when (3n - 1) divided by 9 -


3n - 1 = 9(p) + r, where r is the remainder and p is the quotient.


3n = 9p + r + 1 (II)


Comparing I and II –


r + 1 = 3


r = 2.

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