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

[HmBe]

Homework Statement

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.

 

[haruspex]

Does it help to consider a^c_n-1 mod (6n+1) etc?

 

[Dick]

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?