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Inference of even or odd from the number of divisors?

  1. Mar 31, 2006 #1
    is there some theorem of some sort, that connect the number of divisors of a number to identify if it's even or odd?

    or to be more specific, does number of divisors of a number has any significance in number theory?
     
  2. jcsd
  3. Mar 31, 2006 #2

    shmoe

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    No. Number of divisors depends only on the exponents in the prime factorization of a number, it doesn't care what these primes are.

    Determining if a number is even is not generally a difficult thing to do at any rate.

    Yes, the number of divisors function and many variants are studied extensively.
     
  4. Mar 31, 2006 #3
    what examples of number of divisors function can you give?
     
  5. Mar 31, 2006 #4

    shmoe

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    The basic one counts the number of ways to write n as a product of 2 numbers, you can consider number of ways to write it as a product of k numbers. You can also consider the sum of the divisors, sum of squares of the divisors, etc.
     
  6. Apr 2, 2006 #5

    Gokul43201

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    lqg, look up the following :

    number theoretic functions, the tau function, the divisor function - Mathworld is one place to start

    Note : The number of divisors can tell you whether or not a number is a perfect square
     
    Last edited: Apr 2, 2006
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