
Re: Goldbach Conjecture
Posted:
Sep 17, 2000 3:52 PM


Jan Kristian Haugland <jkhaug00@studNOSPAM.hia.no> a ÃÂÃÂ©crit dans le message : 39C51335.726798CB@studNOSPAM.hia.no... > > > Fred Galvin wrote: > > > On 17 Sep 2000, Daniel McLaury wrote: > > > > > I don't think that Euler would have been fooled by something > > > as simple as x^2 + x + 41. After all, it is obvious that f(41) > > > is 41*43. He may have given this as an example of why not to > > > rely on anecdotal evidence. One of my favorites is the polynomial > > > (x1)(x2)(x3)*...(xn), multiplied out so that its form is not > > > so obvious. Then the prof/teacher says, f(1) = 0, f(2) = 0, ... > > > so therefore f(x) must always equal 0. Half the students are > > > convinced, and then the teacher takes f(n+1) = n!, which is > > > _very_ far from being 0. > > > > A silly example: the "identity" (1+2+3+...+n)! = 1!3!5!...(2n1)! > > which is true for n = 0, 1, 2, 3, and 4, but false for all larger > > values of n. Not in the same league with Euler's x^2+x+41 of course. > > > >  > > "Any clod can have the facts, but having opinions is an art."McCabe > > How about n! = k^3  k where k = 2^(n  3) + 1 > for n = 3, 4, 5, 6? ;) >
Or number of regions from n points on a circle = 2^(n1) for n=1,2,3,4,5 ?
> >

