1
$\begingroup$

Using SageMath I can get the answer:

l=[]
for i in range(1,2000):
    for j in range(i):
        if gcd(j+1,i)==1:
        l.append(j+1)
    if len(l)==4:
        print(i)
        print(l)
    l=[]

Get the result below:
5
[1, 2, 3, 4]
8
[1, 3, 5, 7]
10
[1, 3, 7, 9]
12
[1, 5, 7, 11]

But I can't say it's all the integers, so how should I prove it?

  • 1
    Closely related to all numbers $n$ with $\phi(n)=4$. Should have been answered several times here. I verified that no additional number upto $10^7$ has the property. I do not know the details, but there should be a provable bound far lower than $10^7$ for $\phi(n)=4$ – 2017-02-22

0 Answers 0