10-13-2008, 08:20 AM | #2 (permalink) |
Currently sour but formerly Dlishs
Super Moderator
Location: Australia/UAE
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i couldnt remember this now. been far too long since my uni days. what are you trying to prove? is this homework?
sorry im no help, but theres a heap of highly intelligent people here that could help you.
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An injustice anywhere, is an injustice everywhere I always sign my facebook comments with ()()===========(}. Does that make me gay? - Filthy |
10-15-2008, 01:08 PM | #4 (permalink) |
Junkie
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Ok here you go:
assume that 2^n + 3 ^n - 5^n is divisible by 6 base case: 2^2+3^2-5^2=-12 inductive step: 2^(n+1)+3^(n+1)-5^(n+1) =2*2^n+ 3*3^n -5*5^n =2^n+2^n+3^n+3^n+3^n-5^n-5^n-5^n-5^n-5^n = (2^n+3^n+5^n)+(2^n+3^n+5^n) + (3^n -3*5^n) The first 2 terms are both divisible by 6 (from our assumption) but is the 3rd? We can try induction on that one to prove it assume 3^n -3*5^n is divisible by 6 base case: 3^2 - 3*5^2 = -66 inductive step 3^(n+1) - 3*5^(n+1) =3*3^n - 3*5*5^n =3^n+3^n+3^n-3*(5^n+5^n+5^n+5^n+5^n) =(3^n-3*5^n)+(3^n-3*5^n)+(3^n-3*5^n)-3*2(5^n) =(3^n-3*5^n)+(3^n-3*5^n)+(3^n-3*5^n)-6(5^n) The first 3 terms are divisible by 6 from the assumption and the 4th term is divisible by 6 because it is multiplied by 6. Thus 3^n -3*5^n is divisible by 6 and as a result 2^n + 3 ^n - 5^n is divisible by 6. QED. Please check my work. |
10-15-2008, 08:04 PM | #5 (permalink) |
Currently sour but formerly Dlishs
Super Moderator
Location: Australia/UAE
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does this last post deserve anyhing else but a smily? well done rek...even if it is wrong. well done!
__________________
An injustice anywhere, is an injustice everywhere I always sign my facebook comments with ()()===========(}. Does that make me gay? - Filthy |
Tags |
discrete, induction, math, mathematical |
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