induction proof

I need some help with this induction proof.I'm like stuck at a crucial point and don't know how to get past it and complete the proof (Thinking)

The question says:

Suppose
is a sequence defined as follows :

for all integers
prove that bn is divisible by 4 for all integers n>=1
(Wondering)

Thanks

Quote:

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Originally Posted by NidhiS

yea(Nerd)

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not much to do here.

clearly it is true for , since which is divisible by 4

assume it is true for

then

but and are divisible by 4 by our inductive hypothesis, thus is divisible by 4, since it is the sum of two numbers divisible by 4

the proof is complete

of course you should clean up the proof, it is more of an outline. but i did more than half the work for you

This is what I did:

lets assume that p(k) is divisible by 4 (INDUCTIVE HYPOTHESIS)
so p(k) : bk = bk-1 + bk-2

we have to show that p(k+1) is divisible my 4.

p(k+1) : bk+1 = bk + bk-2
we know that bk is divisible my 4
such that bk = 4l for some integer l

then what next?

er thanks! that actually helped .Let me go back and flip through the pages and see which theorem cna be used to justify this proof.(Happy)

Quote:

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Originally Posted by NidhiS

This is what I did:

lets assume that p(k) is divisible by 4 (INDUCTIVE HYPOTHESIS)
so p(k) : bk = bk-1 + bk-2

we have to show that p(k+1) is divisible my 4.

p(k+1) : bk+1 = bk + bk-1
we know that bk is divisible my 4
such that bk = 4l for some integer l

then what next?

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by the hypothesis, it is true for every for , so the claim is true for as well, so for

thus, ...

well i think you over generalized the proof ,in a way.

er what if k=1 then b 1 = 4l but b0 is not.(Wondering).

I mean b0 is not divisible by 4(Shake)

Quote:

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Originally Posted by NidhiS

I mean b0 is not divisible by 4(Shake)

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doesn't exist, the first term of your sequence is