suneja 2 years ago If n is a positive integer, what is the remainder when 3^(8n+3)+2 is divided by 5? A. 0 B. 1 C. 2 D. 3 E. 4

1. him1618

Split it up into 3^3.3^(8n) +2

2. him1618

Split the second 3 as (5-2)..expand binomially

3. suneja

didnt gt u

4. him1618

binomial expansion aata hai?

5. suneja

@him1618 if u tak n=1 ans is 4 i want does tis hold true for all n

6. him1618

that isnt the way to do it though

7. suneja

then

8. suneja

how to go abt it

9. him1618

like i said remodel it as 27 (5-2)^(8n) +2 expand (5-2) part binomially

10. him1618

when u expand it ull get all terms with a 5 or some power of 5 in them except fr the last one so ure left with 27(5q - 2) +2

11. waterineyes

$$3^{8n}$$ if 3 has powers which are divisible by 4, then Remainder it has is 1.. Here : 8n is divisible by 4..

12. waterineyes

Similary, $$3^3$$ will give you 7 as Unit place..

13. waterineyes

So: $3^{8n} \cdot 3^3 + 2 \implies 1 \cdot 7 + 2 \implies 9$

14. waterineyes

So, what will you get as remainder when you divide 9 by 5 ??