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#1 2008-04-13 06:05:27
- chetah
- Member
- Registered: 2008-02-15
- Posts: 32
Discrete Maths Proves
(a) a and b are members of of the set of positive integers. If b|a and b|(a+2), prove that b = 1 or b = 2.
My solution
b * r = a
b * s = (a+2)
bs = (br + 2)
where do I go from here?
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#2 2008-04-13 06:48:16
- mathsyperson
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- Registered: 2005-06-22
- Posts: 4,900
Re: Discrete Maths Proves
b(s-r) = 2.
s and r are integers, so s-r is an integer.
The only two positive integers that multiply to give 2 are 1 and 2, and so b must be one of those.
Why did the vector cross the road?
It wanted to be normal.
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#3 2008-04-13 07:06:44
- Ricky
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- Registered: 2005-12-04
- Posts: 3,791
Re: Discrete Maths Proves
Do you know the fundamental theorem of arithmetic?
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#4 2008-04-13 07:44:05
- Kurre
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- Registered: 2006-07-18
- Posts: 280
Re: Discrete Maths Proves
Well if b divides a+2, and b divides a, what can you say about the 2 in (a+2)?
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