Recent content by AlexHall

Hello I need to give an example of a function f(x) such that limf(x), as x goes to infinity, exists but the limf'(x) does not. Any help? Thx

I need to show if the following is true or false. If the function f: (0,1)--> R is continuous in every irrational number x then f is continuous at every number. Thank you

Hi I have the harmonic mean H(n) of the divisors of a positive integer n. I need to show that if n is perfect number, then H(n) must be an integer. 1/H(n)={1/τ(n)}Σ(1/d) I have found that H(n)=nτ(n)/σ(n) H(n)=τ(n)/2 How can I conclude that this is an integer? Thank you

phi(n)=phi[2^(k-1)q] where q=(2^k)-1 phi(n)=phi(2^(k-1))phi(q)=phi(2^(k-1))(q-1) Is there any property I can use to finish this?

Hello, can anyone help with this question? Thank you. Let n even perfect number and q prime. Show that n/Φ(n)=2q/q-1. Φ(n) is the Euler function-totient (the number of positive integers less than or equal to n that are coprime to n) I have tried euler-euclid theorem but could not...

Thanks 16!=-1(mod17) 16!=15!.16=-1(mod17) 16=-1(mod17) 15!=1mod17 I don't know how to start the other problems. Any tips?

1) Find the remainder of the division of 15! with 17 2) If (n^2)+2 prime show that 3 divides n 3)If p the smallest divisor for n show that there exist integers a and b such that an+b(p-1)=1 4) For every n>1 show that n does not divide (2^n)-1 Any help?