JMO

For what value of 'n' will the remainder of 351n and 352n be the same when divided by 7?




Answer:

351ⁿ

 (351ⁿ – 1ⁿ)  is always divisible by (351 – 1). Since 350 is divisible by 7 therefore (351ⁿ – 1ⁿ) always divisible by 7.

SO, (351ⁿ – 1ⁿ)/7 = Q, say

So, (351ⁿ – 1ⁿ) = 7Q

Or, 351ⁿ  = 7Q + 1

So, 351ⁿ is divided by 7 it leaves a remainder of 1.

352ⁿ = (7q + 2)ⁿ = (7q)ⁿ+............ + 2ⁿ

352ⁿ/7 = Q1 + 2ⁿ/7

For n = 3 we have a Remainder of 1.

SO, n = 3 Answer