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suneja

  • 3 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

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

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

  3. suneja
    • 3 years ago
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    didnt gt u

  4. him1618
    • 3 years ago
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    binomial expansion aata hai?

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

  6. him1618
    • 3 years ago
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    that isnt the way to do it though

  7. suneja
    • 3 years ago
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    then

  8. suneja
    • 3 years ago
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    how to go abt it

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

  10. him1618
    • 3 years ago
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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

  11. waterineyes
    • 3 years ago
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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..

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

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

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

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