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suneja
Group Title
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
suneja Group Title
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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him1618 Group TitleBest ResponseYou've already chosen the best response.0
Split it up into 3^3.3^(8n) +2
 one year ago

him1618 Group TitleBest ResponseYou've already chosen the best response.0
Split the second 3 as (52)..expand binomially
 one year ago

him1618 Group TitleBest ResponseYou've already chosen the best response.0
binomial expansion aata hai?
 one year ago

suneja Group TitleBest 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

him1618 Group TitleBest ResponseYou've already chosen the best response.0
that isnt the way to do it though
 one year ago

suneja Group TitleBest ResponseYou've already chosen the best response.0
how to go abt it
 one year ago

him1618 Group TitleBest 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

him1618 Group TitleBest 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

waterineyes Group TitleBest 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

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

waterineyes Group TitleBest 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

waterineyes Group TitleBest 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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