quasi
Posts:
9,079
Registered:
7/15/05
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Re: a contradiction worth reading (unless a silly mistake was made)
Posted:
Jul 22, 2011 6:32 PM
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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.
quasi
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