quasi
Posts:
9,076
Registered:
7/15/05
|
|
Re: a contradiction worth reading (unless a silly mistake was made)
Posted:
Jul 24, 2011 12:02 AM
|
|
On Fri, 22 Jul 2011 18:24:04 -0500, quasi <quasi@null.set> wrote:
>On Fri, 22 Jul 2011 17:50:35 -0500, quasi <quasi@null.set> wrote:
>
>>On Fri, 22 Jul 2011 16:11:22 -0500, quasi <quasi@null.set> wrote:
>>
>>>Conjecture:
>>>
>>>If p is prime with p = 3 (mod 4) and (p-1)/2 also prime, then
>>>for all integers x,y with x,y not congruent to 0,1,-1 (mod p),
>>>
>>>the sets
>>>
>>> {x^(2^i) (mod p), i = 1,2,3, ...}
>>>
>>> {y^(2^j) (mod p), j = 1,2,3, ...}
>>>
>>>have the same number of elements.
>>
>>It's true -- I can prove it.
>>
>>But for now, I'll leave it as a challenge.
>
>To Simon Roberts:
>
>The above result, while elementary, is (I think) interesting
>and not entirely trivial, so your ideas did lead to something
>worthwhile.
I take it back -- I've now found a simple, straightforward
proof which makes it clear that proving the above claim is
just a routine exercise.
quasi
|
|
