Loser66
  • Loser66
Find a set of 3 integers that are mutually relatively prime but any 2 of which are not relatively prime.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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zzr0ck3r
  • zzr0ck3r
I am not the best at number theory but I will think on it for a minute.
Loser66
  • Loser66
I post the wrong question, now I correct it. Surely the previous one is easy. :)
Empty
  • Empty
2*3, 3*5, 2*5 ?

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zzr0ck3r
  • zzr0ck3r
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
  • Empty
pq, qr, rp That's a fun more general case. But not like super best.
zzr0ck3r
  • zzr0ck3r
ahh I c. Yeah, what @Empty said
Loser66
  • Loser66
oh oh.... they are integers!! not primes. GGGGGGGGGGGGot it. :)
Loser66
  • Loser66
@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
  • Empty
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
  • Loser66
oh yeah. I am sorry. I should take a snap. :(
zzr0ck3r
  • zzr0ck3r
lol
Empty
  • Empty
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

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