1. OOOVincentOOO

    Audio Analysis Divisor Function

    Hello, The divisor function can be written as a summation of repeating pulses with a frequency. It can be represented with the functions below: $$1) \space \sigma_{0}(x)=\sum_{\mathbb{X}=2}^{\infty} 2^{(-N)} \sum_{k=0}^{N} \binom{N}{k} e^{-i\left( \frac{\pi}{\mathbb{X}}kx \right)} $$ $$2)...
  2. V

    Greatest Common Divisor of two specified sequences of numbers (search for equality)

    I consider two sequences of numbers $A=\{a_1,...,a_n\}$ and $B=\{k-a_1,...,k-a_n\}$, where $a_1 \le a_2 \le ... \le a_n \le k$. I am looking for such conditions under which: $gcd(a_1,...,a_n) = gcd(k-a_1,...,k-a_n)=1$. In more general form: $gcd(a_1,...,a_n) = gcd(k-a_1,...,k-a_n) \ge 1$...
  3. OOOVincentOOO

    Wave Divisor Function

    Dear Math Forum, For quite some time (years), I have been playing around with the divisor function (counting the number of divisors for a given integer). I created a 10 slide summary in the attached presentation. Wave Divisor Function...
  4. M

    factor or divisor

    Is there a difference between divisor or factor of an integer?
  5. J

    Complete divisor of a number

    Hi all, I am having such a naïve problem, yet unable to comprehend it now: 21904/2 should come out to be 1952 plainly, but calculator suggests it to be 10952 . What's the rule here?
  6. D

    divisor chain problem

    Let a divisor chain be a sequence of numbers starting with 1, where each element divides the next. A(n) represents the number of chains ending with n. Prove that the number of odd-lengthed chains O(n) and the number of even-lengthed chains D(n) are either the same or differ by 1.
  7. N

    remainder and a common divisor

    By which number dividing 701, 1059, 1417 and 2312 we will get a common remainder? And what will be that remainder? Please tell me how this problem can be solved.
  8. D

    Find the number of divisors of 189,720 that are composite numbers?

    I have question from my Data Management class that asks for the number of divisors of 189,720 that are composite numbers. I tried to solve the question by using a tree diagram, as I was shown in class. (a) 189,720 4 x 47,430 6 x 7,605 15 x 37, 944...
  9. C

    Greatest Common Divisor

    How to find one of the two numbers if their GCD is 1? For illustration: (a1, N) = 1 where N = 600
  10. P

    Divisor Function

    The classical divisor function is defined as $$\sigma_{\alpha}(s)=\sum_{d|n}\,d^{\alpha}$$ Is there a way to write the following summation $$\sum_{d|n} \log^{k} d $$ using this arithmetic function??? Thanks in advance.
  11. E

    elementary divisor ring

    Can anyone help me? I have a problem with proving a theorem for my thesis. Let R be a Hermite ring. If R/I is an elementary divisor ring, then R is an elementary divisor ring. Is it true? If that's true, I have no idea how to prove that lemma. Please help me.
  12. K

    How do I find the smallest proper divisor of large numbers?

    For example, ( 22! + 1). I can't find examples in books or on the internet. Any help very much appreciated.
  13. B

    Greatest Common Divisor may be NP Complete (if so then P equals NP)

    Clique (graph theory) - Wikipedia, the free encyclopedia (or any of the other interchangible views of NP Complete) has been called the hardest unsolved math problem and would likely result in solving all the remaining millenium problems if P equals NP and that is proven. On the other hand, most...
  14. S

    Summation of all proper divisor

    What is the maximum 4 digit integer n for which the sum of its proper divisors is (n-1)? Thanks in advance
  15. M

    The greatest common divisor

    The greatest common divisor 7571 and 2077
  16. B

    Greatest common divisor of an infinite set

    Hello, help with the following problem would be greatly appreciated: We have an infinite set M =\{n^{13}-n| n \in \mathbb{N}\}, what is the greatest common divisor of all it's members? I have thought about this, and it seems since the power of n is 13 (And the period with which the numbers...
  17. B

    Greatest common divisor proof

    Hello, would someone please help me with the following problem? Even small tips would be welcome. Let x, y, m, n, a, b, c, d be whole integers. The following applies: m = ax + by n = cx + dy ad - bc = 1 Prove that gcd(m,n) = gcd(x,y)
  18. I

    Greatest Common Divisor. Really hard problem.

    There are three different integers: a,b,c > 1 which satisfy the condition GCD(a,b,c)=1. Find all possible values ??for GCD(a^2b+b^2c+c^2a, ab^2 +bc^2 +ca^2, a+b+c) I know that problem can be difficult, but I would be very grateful for any help. :D
  19. M

    greatest common divisor

    Hello I have problem with finding the every possible value of number x, y, z \in Z GCD(x^2y+y^2z+z^2x, xy^2+yz^2+zx^2, x+y+z) when x,y,z > 1 and GCD(x, y, z) = 1 any ideas how to start?
  20. M

    Divisor function and Dircihlet

    So I have constructed a table of all the non principal Dirichlet characters mod 16. Here is said table: Now, for each real-valued nonprincipal character ? mod 16, I want to veryify that: A(225) ? 1. A(n) = \Sigma ?(d) d|n Can anyone help? Thanks Here is the table mod 16...