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Find all pairs (a,b) of integers
such that
Last edited by tony123 (2009-09-04 12:39:25)
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I don't believe there are any integers because...
Last edited by Fruityloop (2009-09-05 13:32:52)
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Hi;
There are at least 2 solutions in Z
a=18 , b=3
a=3 , b=18
There may be more...
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Good job Bobbym!
Oops...boy was I wrong.
(a+b)(a^2-ab+b^2)=3(2007-ab) doesn't mean (a+b)=3 or (a^2-ab+b^2)=3
Last edited by Fruityloop (2009-09-06 00:54:52)
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Hi Fruityloop;
I am stuck on this one too.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Hi Tony123;
Prove:
That shows that 6021 can be factored into an integer square and another term. Also there are no negative solutions (If b were negative b^2 would of course be positive)
We could either try all 8 factors 2 at a time or notice that one factor has to be a square. Only 1 and 9 are possible. 1 doesn't work but 9 does. b^2 = 9 -> b=3.
The only solutions are:
3,18 and 18,3.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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