FERMAT theoram

[phanbachloc]

for n>2 ; x^n+y^n=z^n will not have any x,y,z to satisfy,wont it?
is it proven so?
what 's the largest primenumber?

[bugzpodder]

yes its proven by Andrew Wiles in 1993 or so.there is no non-trivial integral solution to x^n+y^n=z^n, n>2

as NotLKH pointed out, solutions exists when x=0, y=0 and/or z=0

what 's the largest primenumber?

?? what do you mean by that?

[snakeeyes1000]

there is no one largest prime number. I have a prog that finds a lot of primes(all up to 2000000000) that saves them all to file. Reply if you want it. It takes hours to run. I would let it go overnight. Takes 500 megs on hard drive, 50 diff files 10mb each

[NotLKH]

Originally posted by bugzpodder
.....execept when x=y=z=0

How about z=t, x = 0, y=t {Or, z=t, x=t, y=0}
where t is any positive integer, for all n,
{or, also, when n is even:
z=(-1)^k1*t, x = 0, y = (-1)^k2*t
where k1,k2 are Positive integers}
Such as {x,y,z} = {0,1,1}:

0²⁹+1²⁹=1²⁹

[bugzpodder]

ok, make that "no positive integral solution"

dicitionary definition says "no non-trivial integral solution"

[NotLKH]

Consider it made.


Just felt like pointing out that x=y=z=0 isn't the only trivial solution, as you suggested, but that {0,1,1} is also one, as is {0,t,t} For all n, and {0, +/-t, +/-t} for all even n.

{Although I don't see why we have to leave the non-trivial definition}

[phanbachloc]

but as i know theres largest primenumber.found by Cameron,and i wonder how can he find it?

[bugzpodder]

he found the largest Mersenne prime, 2^134966917-1

a mersenne prime is a prime that has the form 2^p-1

here is the proof that there is infinitely many prime numbers:

assume all primes in the world are p1,p2,...,pn

now let q=p1*p2*...*pn+1
now, q mod p1=q mod p2=...=q mod pn=1
(q mod any prime number p1,p2,...,pn is congruent to 1)

so q is not divisible by any prime number other than 1 and itself.

thus q is prime.

therefore there is an infinite # of primes

[phanbachloc]

can we do that on my own computer?or linux based one?

[SteveCRM]

Originally posted by phanbachloc
for n>2 ; x^n+y^n=z^n will not have any x,y,z to satisfy,wont it?
is it proven so?
what 's the largest primenumber?

thats true

I haven't read the other posts so Im not sure if they answered this. Some guy spent about 12 years proving it but he finally did it. And there is no one largest prime numbers, there is an infinite amount.

[SteveCRM]

Originally posted by phanbachloc
can we do that on my own computer?or linux based one?

I think the guy that ran that program made a very very complex program that ran over his christmas break on the university servers. So it took those servers about 2 weeks to come up with that.

[jim mcnamara]

Phan -

"You give me the largest known prime number. I can always find a bigger one. " -- this is what the posters are telling you.

This is what Cameron et al did:

You wanna do this, too? go to the Mersenne prime org site and download the free software. You need a 1GHz PC or so ans about 10-12 weeks of free time on the PC.

http://www.mersenne.org/prime.htm

[phanbachloc]

will we find out the number larger than 2^134966917-1 in 12-13 weeks?

[bugzpodder]

there is literally at least of thousands ppl doing this. and only 3 ppl who ran the program found those primes. u do the math. whats the probability that u find one? btw if u find one thats over 10 million digits long, you'll get some $$$

[phanbachloc]

why dont u find it for some $$$$?

[phanbachloc]

do we need to set my computer online all the time?