On dividing a positive integer n by 9 we get 7 as a remainder. what will be the remainder is 3n-1 is divided by 9
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Let q be the quotient.
It is given that: Remainder = 7
On applying Euclid’s algorithm, i.e. dividing n by 9, we have n = 9q + 7 ⇒ 3n = 27q + 21 ⇒ 3n – 1 = 27q + 20 ⇒ 3n – 1 = 9 × 3q + 9 × 2 + 2 ⇒ 3n – 1 = 9 × (3q + 2) + 2
So, when (3n-1) is divided by 9, we get the remainder 2 .
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