Hello!
The following question was asked in a Soviet Union mathematics Olympiad about 2-3 decades ago. A friend brought it up a few days ago and it has been bugging us since then.
The problem goes along the lines of:
"There are 10 ammo boxes each containing 10 bullets, and each bullet...
Well first of all, thank you to all for making it clear to me that the ratio doesn't necessarily have to be an integer. I actually showed this to a mathematics professor at my school, and my argument actually convinced them! That's why I thought that part was correct...
And by the way...
I disagree... let's assume there could be integers a, b, and c not equal to each other that will satisfy the equation when multiplied out.
Let's take for example the first part: a2/(bc)n = xα
xα will never be an integer, do you agree? This would also be the case for b2/(ac)n = yβ, and c2/(ab)n...
You can also view this image: http://www.freeimagehosting.net/j8qzj
This is what the theorem states:
"No three positive integers a, b, and c can satisfy the equation a^p+b^p=c^p, for any integer values of p >2"
My attempt (p = n+2 > 2):
ap+bp=cp
a(n+2)+b(n+2)=c(n+2)
(an*a2...