Re: Puzzled (4^162 mod 100)

In article <CoXXf.12775$6Q2.198755@weber.videotron.net>,
Carlos Moreno <moreno_at_mochima_dot_com@mailinator.com> wrote:
>Sebastian Gottschalk wrote:
>> Carlos Moreno wrote:
>>
>>>I stumbled into this exercise in number theory, and I'm
>>>clueless about what is the "correct" way to solve it.

>> 4^162 mod 100 = 4^(162 mod phi(100)) mod 100 = 4^(162 mod 40) mod 100 =
>> 4^2 mod 100 = 16 mod 100
>>
>> Dude, that's so simple you should go away and sink down in shame because
>> you didn't even listen at your lessons.
>
>Is this like the most ironic thing I've seen this year, or
>is it still April 1st and my clock is going too fast? Or
>was I *really* not listening?
>
>The above (based on Euler's Theorem, if memory serves) is
>applicable only if the base and the modulo are relatively
>prime -- 4 and 100 are not relatively prime, so Euler's
>theorem does not say anything applicable to this problem.
>
>Right?

It does not say anything directly. It, does, however, say
->something<-. See my post to see why Sebastian Gottschalk's assertion
can be justified... though I do not think in quite as cavalier a
manner as he didd.

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu