Recent content by joshuathefrog

That should have read phi(65) = 48.

I figured out my mistake. I was letting l=1 when really I meant that l=2. I know that phi(60 = 48, so I divide the right side by 48 and divide the left side by phi(60). That solves the problem. Just a stupid mistake. But thanks for the help!

I tried integrating your function using a TI-89, and I come up with a definite integral of (√6) / 6 when evaluated from 0 to 1. The indefinite integral is quite long ...

Sigh ... yes. Yes I can. I think it's time for a break, I've been staring at this for too long and I'm starting to forget about basic math. Thanks for the wake up call!

Another thought here: I have that l=1, m=7, and n=3, such that phi(23)*phi(57)*phi(13) = 26 * 56 * 13 * 3. I want to divide the 3 out so that I am only left with the prime factorization of 13,000,000 on the right hand side. However, there does not exist a y such that phi(y) = 3...

I can use Euler's theorem since 13 and 50032 are coprime. However, I then end up with: 13phi(50032) = 1 mod 50032. How can I manipulate this so that I have 13 mod 50032 instead of 1 mod 50032?

Homework Statement Find an integer x that is a solution (only need one solution, not all solutions). If no solution exists, prove that no solution can exist. 13x = 13 mod 50032 , with x > 1. Note that 5003 is prime. Here, = means "congruent to" Homework Equations Not sure. I can solve...

I'm trying to solve other problems of the same type. I have that phi(x) = 13,000,000. Since the prime factorization of 13,000,000 is 265613, I wrote that phi(2l)phi(5m)phi(13n) = 2l-1(1)5m-1(4)13n-1(12). I can express 4 as 22, but 12 = 3*22, and I don't see how to get 3 out of the...

Fantastic! Thanks for the help!

Ah, ok. So, I think that if I let p=2 and q=5, and m=5 and n=8, then phi(2558) = 24(1)57(4) = 245722 = 2657 = 5,000,000. So, my answer would be x = 2558. Look ok?

Since phi is multiplicative, I could say that phi(26)*phi(57) = 25(1) * 56(4) = 32(15625)(4) = 2,000,000. Would this be going in the right direction towards a solution?

Thanks for the response. I don't have to find ALL solutions to the problem. I just need to find one solution, or, if no solutions exist, prove that no solutions exist. I know that the prime factorization of 5,000,000 is 26 * 57. But, I don't yet see what I can do with this information.

Homework Statement Find x such that phi(x) = 5,000,000, where phi(x) is Euler's function. Homework Equations I know that if x is prime, then phi(x) = x-1. Also, phi(pk) = pk - pk-1 = pk * (1 - 1/p). The Attempt at a Solution Since 5,000,001 is not a prime number...