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suneja

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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  1. him1618
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    Split it up into 3^3.3^(8n) +2

    • one year ago
  2. him1618
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    Split the second 3 as (5-2)..expand binomially

    • one year ago
  3. suneja
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    didnt gt u

    • one year ago
  4. him1618
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    binomial expansion aata hai?

    • one year ago
  5. suneja
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    @him1618 if u tak n=1 ans is 4 i want does tis hold true for all n

    • one year ago
  6. him1618
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    that isnt the way to do it though

    • one year ago
  7. suneja
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    then

    • one year ago
  8. suneja
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    how to go abt it

    • one year ago
  9. him1618
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    like i said remodel it as 27 (5-2)^(8n) +2 expand (5-2) part binomially

    • one year ago
  10. him1618
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    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
  11. waterineyes
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    \(3^{8n}\) if 3 has powers which are divisible by 4, then Remainder it has is 1.. Here : 8n is divisible by 4..

    • one year ago
  12. waterineyes
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    Similary, \(3^3\) will give you 7 as Unit place..

    • one year ago
  13. waterineyes
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    So: \[3^{8n} \cdot 3^3 + 2 \implies 1 \cdot 7 + 2 \implies 9\]

    • one year ago
  14. waterineyes
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    So, what will you get as remainder when you divide 9 by 5 ??

    • one year ago
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