Hello All, New Person Here

[bloodhound]

Anyway. I am a Maths Student at University of Nottingham. Just about to finish my first year. Have exams in may/june. Ok then. introductions over, ill give u a started question:

 

Find all integer solutions for a^b=b^a given that 0<a<b.

 

Its a really nice question I found in a book. It has a nice solution as well.

 

ooh dont bother with that question. i see that its been asked in other sub forums

 

HEHE

 

anyway later

[bloodhound]

Since pple have asked this question before in other forums. ill post my solution to it anyway

 

take a function f where f (x)=ln(x)/x

therefore a^b=b^a if and only if f(a)=f(b). now differentiating f(x) u will find that there is a maximum at x=e. therefore the function f is increasing for x<e and decreasing for x>e. therefore its not possible for both a,b <e or a,b >e cos then f(a) will never be equal to f(b) for a<b

so the only solutions possible is a<e and b>e . now we have 0<a<e. and a is an integer. therefore a=1 or a=2. putting in a=1 we get b=1 which is not a solution as we need a<b. the only other soultion is a=2. puting in a=2 and solving f(b)=f(2) by similar method or however u want we get b =4 . therefore the only solution to a^b=b^a for 0<a<b is a=2,b=4

[Dave]

At last, a solution

 

That one's been plaguing the forums for a while now, cheers.

 

(ditto btw, I'm a first year at warwick).

[bloodhound]

glad to be of some help. hows maths in warwick. i heard its one of the best. was having a look at some of u problems in the competition sections. quite good questions.

[Dave]

Bloody tough But then again, I suppose it's going to be the same kindof experience no matter where you go.

[bloodhound]

Maths is Nottingham is also one of the best if u look at the tables. The timetable is very light though. so thats good. i have a fren who studies maths at imperial. also another frens roommate also does maths. and when i look at the work they get and their timetable, i thank god that i went to nottingham.

[Dave]

Our timetable's pretty crammed. Last term, I had 9am-6pm with a 1 hour break in the middle, average about 25 contact hrs per week.

[bloodhound]

lol . thats a lot.

 

I have about 11 hrs a week of lectures and about 3 hours of problem class and 1 hour group tutorial a week. but i never go. i got told off for not attending problem classes at all.

[Dave]

git

[bloodhound]

yeah. its pretty relaxed. love it. i think the second year goin to be tough.

[Dave]

Definately, especially with the amount of modules I have to do, plus an essay that lasts 2 terms.

[bloodhound]

i hope i wont have to do any essays. are u doing a MMath course? apparently the whole 4th year we spend doing a thesis. phew. ill probably do it the night before

[Sayonara]

Oh lordy; now there are two of them.

 

[bloodhound]

is that a bad thing sayonara?

[Dave]

i hope i wont have to do any essays. are u doing a MMath course? apparently the whole 4th year we spend doing a thesis. phew. ill probably do it the night before

 

Yeah, I'm on the MMath. Whether I'll stay on it or not I'll see, but I doubt you'd be doing something that large the night before ;-)

[bloodhound]

so whats ur fav module rite now then

[Dave]

Favourite module would be analysis, followed pretty closely by linear algebra.

[bloodhound]

yeah. same here. analysis is wicked. followed probably by calculus

[bloodhound]

do u have to use maple. and have u got it?

[Dave]

We've had to do a module of Matlab, which sucked.

[bloodhound]

dont know about MatLab but Maple is Wicked