Find a set of 3 integers that are mutually relatively prime but any 2 of which are not relatively prime.

Question

Find a set of 3 integers that are mutually  relatively prime but any 2 of which are not relatively prime.

zzr0ck3r · Answer

I am not the best at number theory but I will think on it for a minute.

loser66 · Answer

I post the wrong question, now I correct it. Surely the previous one is easy. :)

empty · Answer

2*3, 3*5, 2*5 ?

zzr0ck3r · Answer

Let $d$ be a common divisor of $a+b$ and $a−b$, then $d$ divides their sum $2a$ and difference $2b$. If a number divides two numbers it also divides their gcd, thus $d$ divides $2gcd(a,b)=2$. That implies that every divisor (including the greatest common divisor) is a divisor of $2$.

empty · Answer

pq, qr, rp

That's a fun more general case. But not like super best.

zzr0ck3r · Answer

ahh I c. Yeah, what @Empty  said

loser66 · Answer

oh oh.... they are integers!! not primes. GGGGGGGGGGGGot it. :)

loser66 · Answer

@Empty  your set doesn't work :(
2*3, 3*5, 2*5 = 6, 15, 10 , they are not mutually relative prime nor pair-wise relative prime

empty · Answer

They are mutually relatively prime because:

$$gcd(6,10,15)=1$$

but any two are NOT relatively prime:

$$gcd(6,10)=2$$$$gcd(6,15)=3$$$$gcd(10,15)=5$$

That's what you asked for!!

loser66 · Answer

oh yeah. I am sorry. I should take a snap. :(

zzr0ck3r · Answer

lol

empty · Answer

Haha it's ok! This is a fun problem but it's confusing! xD 

Honestly anything with 'relatively prime' in it makes my head spin a little bit ahaha