Re: proving something is an integer

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Re: proving something is an integer

Paul Sperry	30 Sep 2005 03:04
> Hi, > [quoted text clipped - 6 lines] > > where n >= 0 is an integer. > [...] No matter what, -1 is a root of x^(2n + 1) + 1 so x + 1 is a factor. Let x = p (or any other integer). Signature Paul Sperry Columbia, SC (USA)

cndc

30 Sep 2005 01:35

Hi,

Let p be a prime number. I need to show that

2n+1
p + 1
K = ---------------
p + 1

where n >= 0 is an integer. This seems to work fine with examples

(i.e. (5^3 + 1)/(5+1) = 21)

but I'm not sure how to show this. Induction on n:

Case 0:
0 + 1
p + 1
----------------- = 1
p + 1

inductive step:

suppose it is true for k,

2k+1
p + 1
---------------
p + 1

we need to show it is true for k + 1:

2(k + 1) + 1 2k + 3
p + 1 p + 1
------------------------ = ------------------
p + 1 p + 1

but I don't see how to work the induction hypothesis in there.

The formula seems reminiscent of the Fundamental Theorem of Algebra
but I don't see how to use it.

Thank you,
-e

Re: proving something is an integer

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