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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
 one year ago
 one year 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
 one year ago
 one year ago

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him1618Best ResponseYou've already chosen the best response.0
Split it up into 3^3.3^(8n) +2
 one year ago

him1618Best ResponseYou've already chosen the best response.0
Split the second 3 as (52)..expand binomially
 one year ago

him1618Best ResponseYou've already chosen the best response.0
binomial expansion aata hai?
 one year ago

sunejaBest ResponseYou've already chosen the best response.0
@him1618 if u tak n=1 ans is 4 i want does tis hold true for all n
 one year ago

him1618Best ResponseYou've already chosen the best response.0
that isnt the way to do it though
 one year ago

him1618Best ResponseYou've already chosen the best response.0
like i said remodel it as 27 (52)^(8n) +2 expand (52) part binomially
 one year ago

him1618Best ResponseYou've already chosen the best response.0
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
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
\(3^{8n}\) if 3 has powers which are divisible by 4, then Remainder it has is 1.. Here : 8n is divisible by 4..
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
Similary, \(3^3\) will give you 7 as Unit place..
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
So: \[3^{8n} \cdot 3^3 + 2 \implies 1 \cdot 7 + 2 \implies 9\]
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
So, what will you get as remainder when you divide 9 by 5 ??
 one year ago
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