Fair fax county mathmatics league

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The discussion revolves around solving the mathematical problem of finding ordered pairs of integers (a, b) that satisfy the equation a^b = b^a, given that a < b. Participants suggest experimenting with small integers to find solutions. One participant successfully identifies the pair (2, 4) as one of the solutions. The conversation highlights the challenge and excitement of solving such mathematical problems. Overall, the problem fosters engagement and collaborative problem-solving among participants.
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Ah...

This problem is very interesting.

but,, I don't know how to solve it... T,T

"If a<b, what are both ordered pairs of integers (a,b) which

satisfy a ^b = b ^ a ?"
 
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Yes, that is a very interesting problem. The first thing I would do is start experimenting with a and b small integers. Have you done that? If so, one of the two pairs should come immediately and the other is not too difficult to find.
 
yay! i got it! is it two and four?
ah! i should have got this question before..T.T anyways thank you><
 
(2,4) is one of the two pairs ...
 

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