Carmichael numbers of the form (6n+1)(12n+1)(18n+1)

  • Thread starter Thread starter HmBe
  • Start date Start date
  • Tags Tags
    Form Numbers
HmBe
Messages
45
Reaction score
0

Homework Statement



q-1.png


Homework Equations





The Attempt at a Solution



I'm fine with the second part (n = 6). But the first part is eluding me, I've been told it's quite simple.

I feel like it's something to do with the fact that for each prime factor of C_n, p1, p2, p3, we have

p-1|C_n-1

But don't really know how to use this.
 
Physics news on Phys.org
Does it help to consider acn-1 mod (6n+1) etc?
 
Pick a so that gcd(a,c_n)=1. So gcd(a,p1)=1. So a^(p1-1)=1 mod p1. See a good place to use your divisibility fact?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

The only prime of the form n^3-1 is 7?
Replies
2
Views
4K
The only prime of the form n^2-4 is 5?
Replies
2
Views
3K
Difficult number theory problem proofs
Replies
3
Views
2K
Comp Sci Finding Cousins of Giuga Numbers: Can You Solve This Prime Number Puzzle?
Replies
32
Views
4K
Relatively prime proof involving a^n and b^n
Replies
3
Views
2K
Prove that if p > 3 is a prime number, then p^2 = [....]
Replies
16
Views
2K
Is Any Carmichael Number Divisible by a Perfect Square Greater Than 1?
Replies
1
Views
2K
Prove that if three numbers have no prime factor in common...
Replies
10
Views
2K
Prove ##|\{ q\in\mathbb{Q}: q>0 \} |=|\mathbb{N}|##.
Replies
3
Views
2K
Prime factors of odd composites
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top