Re: Q's on Number Theory/Quadriatic Residues

[Ben <samman@cs.yale.edu>]

At 05:47 PM 8/13/95 PDT, Derek Atkins wrote:
>>                  -1             -1
>>         v       v         sqrt(v  )
>>          16      11           ***9
>>          29      29           ***8
>> 
>> ***How are these square roots?  9 is certainly not the square root of
>> 11, nor is 8 the square root of 29, even modulo 35.
>
>Bzzt!  Try Again.  If you use bc, you will notice that 9^2 mod 35 == 11
>and 8^2 mod 35 == 29...  You should go take your number theory class!

Definitely. Is there an easy way to get from the 29 to the 8?  I can see how
it goes
the other way, but what I didnt' see was how, if given 29, I could get the
8? (Euclid's?)

>
>>         mean "the inverse of v."  Are these two expressions interchangeable
>>         or is this something that I should have found in the errata?
>
>Yes.  It is the multiplicative inverse.  This is very basic math.  Go
>re-read your 7th-grade algebra book:
>	v^(-1) == 1/v

Ok.  I wasn't thinking of multiplicative inverse when doing this--I guess I
wasn't in the right frame of mind.

>Take your number theory class, and if you can't figure out after that,
>re-ask the questions.

I'll take the course, but you still needn't be so swarmy about it.

Ben.
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Ben Samman					     Samman@cs.yale.edu
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