Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
#1 2009-09-05 10:38:54
- tony123
- Full Member
Offline
Find all pairs
Find all pairs (a,b) of integers
such that
Last edited by tony123 (2009-09-05 10:39:25)
#2 2009-09-06 11:25:04
- Fruityloop
- Full Member
Offline
Re: Find all pairs
I don't believe there are any integers because...
Last edited by Fruityloop (2009-09-06 11:32:52)
Help slow global warming. Drive a prius.
July 2012 was the hottest month ever for the U.S.
#3 2009-09-06 15:24:19
- bobbym
- Administrator
Online
Re: Find all pairs
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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2009-09-06 22:46:48
- Fruityloop
- Full Member
Offline
Re: Find all pairs
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 22:54:52)
Help slow global warming. Drive a prius.
July 2012 was the hottest month ever for the U.S.
#5 2009-09-06 23:11:47
- bobbym
- Administrator
Online
Re: Find all pairs
Hi Fruityloop;
I am stuck on this one too.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#6 2009-10-28 04:20:20
- bobbym
- Administrator
Online
Re: Find all pairs
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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.