anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Split it up into 3^3.3^(8n) +2
anonymous
  • anonymous
Split the second 3 as (5-2)..expand binomially
anonymous
  • anonymous
didnt gt u

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anonymous
  • anonymous
binomial expansion aata hai?
anonymous
  • anonymous
@him1618 if u tak n=1 ans is 4 i want does tis hold true for all n
anonymous
  • anonymous
that isnt the way to do it though
anonymous
  • anonymous
then
anonymous
  • anonymous
how to go abt it
anonymous
  • anonymous
like i said remodel it as 27 (5-2)^(8n) +2 expand (5-2) part binomially
anonymous
  • anonymous
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
anonymous
  • anonymous
\(3^{8n}\) if 3 has powers which are divisible by 4, then Remainder it has is 1.. Here : 8n is divisible by 4..
anonymous
  • anonymous
Similary, \(3^3\) will give you 7 as Unit place..
anonymous
  • anonymous
So: \[3^{8n} \cdot 3^3 + 2 \implies 1 \cdot 7 + 2 \implies 9\]
anonymous
  • anonymous
So, what will you get as remainder when you divide 9 by 5 ??

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