Fermat's Last Theorem
How many solutions ( a , b , c , n ) are there to the equation
a n + b n = c n
for n > 2 ?
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3 solutions
But that is a trivial solution.
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There were never constraints put on the variables, besides n.
when you let a=b=c=0.
I think fermat's last theorem is valid for only positive integers
For any choice of a , b , n if c = n a n + b n then the equation is satisfied. Since there are uncountably infinitely many choices for a , b , n , the solution set is uncountably infinite.
April Fools
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Awww, got me there :( Learned my lesson to read problems more accurately.
WHY IS FERMAT"S LAST THEOREM IN THE TITLE!!!!! I was totally fooled by this one.
Ohh please!? It's really not a good joke. I'm in level 5 and lost lots of ratings by assuming this question as a real Fermat's Last Theorem . At least in the title you can add a question mark or you could make this as an unrated problem . If it is permitted on Brilliant, I can also do the same thing as an April Fools's prank but I will NOT do such thing as that. Grow up kid!
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This question is unrated as on 4/2/2014 7:54 PM IST. How did you lose your rating?
Why are you blaming the author of the question for your own mistake?
Though the title is somewhat misdirecting, you could have solved it correctly if you had read the question properly.
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You may want to take a look this:
As you can see this was a
rated problem
.
Now, you see this note by Calvin: How To Get Your Problem Shared/Liked On Brilliant . Read point no. 1: Simplify your statements and state them precisely. Do not try to be tricky , point no. 4: Choose a title which reflects the content of the problem , and then point no. 9: Avoid any ambiguity; define uncommon terms .
Now, imagine this one: How if there are other members also make problems like this as a prank ?? You as a level 5 member definitely know how hard a level 5 member earn points or maintain his rating. Read also this note by Michael Mendrin: A problem for Level 5 users in solving low Level problems .
I'm sorry for making the problem rated, I did not realize that I could make it unrated. I had no intention of causing people to lose their most important, meaningful, hard earned ranks, but I now realize the consequences of my actions. I will reevaluate my maturity and hopefully one day take your advice and finally grow up.
No need to be so angry. We are here to enjoy and share problems not bicker about petty levels and ratings..
This problem is better taken as a lesson for us. Calm down.
oh wait darn yeah they dont have to be integers... =p >=(
Aw i thought it was the real fermat last theorem :( you got me there
Wait, so is 'Uncountably Infinitely Many' correct? I know that it's supposed to be a fool question and all, but WHAT IF YOU MAKE OTHER PEOPLE LOSE RATING D: So is the correct answer indeed 0?
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Oh.... It doesn't have to be positive integers. WHY YOU PUT FERMAT'S LAST THEOREM IN TITLE!!! D:
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@Math Calculus – April fools! Always assume the domain over the reals unless otherwise specified.
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@Trevor B. – According to whom?
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@Oliver Bel – Rule of thumb, it's certainly not a law.
@Oliver Bel – Never assume anything in math.
For example, in the heading of AP Calculus tests and most of the math competitions I've been in, it was said in the heading of the paper that the domain of all functions is the real numbers unless otherwise specified.
Be glad that it is now unrated. This is the worst April Fools joke ever, considering that it does damage to someones hard-earned rating.
Taking a = b = c = 0 we get 0 n + 0 n = 0 n which is satisfied when n is a non-zero real number. So, it has uncountably infinitely many solutions.