## mod or binomial

For discussing Olympiad Level Number Theory problems
the arrivals
Posts: 41
Joined: Tue Dec 21, 2010 10:17 pm

### mod or binomial

what if you are asked at the olymiad question what will be the remainder if (2^1990) is divided by 1990
i perhaps write there are very good programmes wriiten for this.the studip question setter should try this if he has got really that much interest
another interesting problem is perhaps like this
suppose you are quite good in multiplication.that means you know quite a good sort of techniques to multiply two numbrs quickly.
now a question perhaps be set like this
consider
the number below
X=(9999999999999999)(9999999999).
which of the given numbers divides X
1)12
2)999
3)289
4)23
5)187
but wait the question setter gives this clue
USE FERMATS LITTLE THEOREM i mean FLT
seeing this question believe me i ll just jumped out but in the same time ofcourse silently i ll condemn the setter
ok no problem for the students of BANGLADESH.cause i believe they are
women of purity are for men of purity and hence men of purity are for women of purity - THE HOLY QURAN

Moon
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
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### Re: mod or binomial

First of all, I would like to ask you, if this part is supposed to be a joke, what actually is the joke part of this post. (Probably I lack sense of humor.)

If that was supposed to be a criticize then I must say that you should think a bit before criticizing someone (and saying someone stupid whom you don't even know). First of all, this problem is not stupid. Though I am not a fan of this type of computation problems, this can be solved with some technique. (I guess you heard of CRT.)

Second, I am not sure if that was a problem from an Olympiad (I might not be right, though).

Please clarify what you tried to mean in your last post,in case I have misunderstood something.

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"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin