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Math Help - Proof by contradiction

  1. #1
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    Proof by contradiction

    I am having difficulty with the following question: ( see attachment)
    I tried expanding it and i still didnt seem to quite get it.
    Any help would be apriciate, thanks in advance.
    Proof by contradiction-capture.jpg
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  2. #2
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    Quote Originally Posted by kensington View Post
    I am having difficulty with the following question: ( see attachment)
    I tried expanding it and i still didnt seem to quite get it.
    Any help would be apriciate, thanks in advance.
    Click image for larger version. 

Name:	Capture.JPG 
Views:	36 
Size:	15.9 KB 
ID:	20988

    Induction on n is a straighforward way, but you can do as follows as well:

    3^{4n+2}+1=9\cdot (3^4)^n+1=9\cdot (81)^n+1 , and you're done since 9 times a

    number ending in 1 ends in 9...

    Tonio
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  3. #3
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    If you want to do it by induction here is a trick.
    3^{4(n+1)+2}+1=3^{4(n+1)+2}+3^4-3^4+1=3^4(3^{4n+2}+1)-3^4+1
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  4. #4
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    Quote Originally Posted by Plato View Post
    If you want to do it by induction here is a trick.
    3^{4(n+1)+2}+1=3^{4(n+1)+2}+3^4-3^4+1=3^4(3^{4n+2}+1)-3^4+1
    So how does that show its divisible by 10? im a little confused
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  5. #5
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    Quote Originally Posted by kensington View Post
    So how does that show its divisible by 10? im a little confused
    The first term is divisible by 10 by the inducutive hypothesis, and you can just add up the last 2 terms to see that it ends in a 0.
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  6. #6
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    Wonder why the topic says "Proof by contradiction " ?? By induction you mean ?
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