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Hi Guys
There is another question. Go ahead & give me your explanations

If n is a positive integer, what is the remainder when 3^(8n+3) + 2 is divided by 5 ?
Answer choices - 0,1,2,3,4

RishiRaj wrote:
Hi Guys
There is another question. Go ahead & give me your explanations

If n is a positive integer, what is the remainder when 3^(8n+3) + 2 is divided by 5 ?
Answer choices - 0,1,2,3,4

Hi Rishi,

As usual. Big numbers involved, so there has to be a pattern..Here's the solution:

Since 3 ^ (8n + 3) will always have 7 as the last digit, the whole _expression_ will always have 9 as the last digit. This _expression_ when divided by 5, will always have the remainder as 4.

So, the answer must be 4.

Please ask for clarification if any...

Hi RishiRaj,

To solve this question we need to understand the repeating pattern for the sequence of powers of 3.

Lets See:

3^1 = 3 ; 3^2 = 9 ; 3^3 = 27 ; 3^4 = 81
3^5 = 243 ; 3^6 = 729 ; 3^7 = 2187 ; 3^8 = 6561 .....& so on.

Here if one observe closely he'll come to know that the last digit or the Unit's digit repeat itself after every 4 powers.

so in 3^n if

n= 4p ; the unit's digit will be = 1
n= 4p+1 ; the unit's digit will be = 3
n= 4p+2 ; the unit's digit will be = 9
n= 4p+3 ; the unit's digit will be = 7


in given question {3^(8n+3)} + 2

The unit's digit in 3^(8n+3) will be - 7

& Units digit in {3^(8n+3)} + 2 will be = 7+2 =9

Hence, if we'll divide it by "5" the remainder will be "4".