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Thread: A problem about number theory

  1. #1 A problem about number theory 
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    Hey, I am sticked by a problem about number theory, i hope someone can give me some hints or steps on it.

    Here is the problem, let p=2^n+1, show that n must be even.
    And if p=2^n+1, and 3^((p-1)/2)=-1(mod p) show that p is a prime.

    I tried to let when n is odd, p=2*2^k+1 and try to find the divisiors, but i failed

    Also, for the second problem, i used the quardratic reciprocity law to do this problem but it seems not working.

    Thanks for helping me guys!


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  3. #2 Re: A problem about number theory 
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    Quote Originally Posted by ryancheng
    Hey, I am sticked by a problem about number theory, i hope someone can give me some hints or steps on it.

    Here is the problem, let p=2^n+1, show that n must be even.
    And if p=2^n+1, and 3^((p-1)/2)=-1(mod p) show that p is a prime.

    I tried to let when n is odd, p=2*2^k+1 and try to find the divisiors, but i failed

    Also, for the second problem, i used the quardratic reciprocity law to do this problem but it seems not working.

    Thanks for helping me guys!
    This has all the earmarks of a homework problem in a class on elementary number theory.

    You need to do your own homework assignments.


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  4. #3  
    Forum Masters Degree organic god's Avatar
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    This has all the earmarks of a homework problem in a class on elementary number theory.

    You need to do your own homework assignments
    he is asking for hints and steps, not a solution.

    Surely this is something the forum can do
    everything is mathematical.
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  5. #4  
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    I am not going to do your homework either, especially as I loath number theory. But I cannot resist the temptation to ask if you posed the question as it was asked. Consider which is clearly prime.

    Or have I misunderstood something?
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  6. #5  
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    Quote Originally Posted by Guitarist
    Or have I misunderstood something?
    You have not so much misunderstood something as failed to realize it for what it is. This is what it is:


    (Prove this by induction.) A positive integer that is divisible by 3 obviously canít be prime unless it is equal to 3 itself.
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  7. #6  
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    Quote Originally Posted by JaneBennet
    Quote Originally Posted by Guitarist
    Or have I misunderstood something?
    You have not so much misunderstood something as failed to realize it for what it is. This is what it is:


    (Prove this by induction.) A positive integer that is divisible by 3 obviously canít be prime unless it is equal to 3 itself.
    Even easier , 4 is congruent to 1 mod 3, 2 is congruent to 2 mod 3 so is congruent to 2 mod 3 and hence is congruent to 3 mod 3.

    It is largely for this reason that I concluded that the OP was asking for homework help and he needed to do the work himself. This is so simple that any hint is tantamount to handing him the answer.
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