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Loser66

  • one year ago

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

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  1. zzr0ck3r
    • one year ago
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    I am not the best at number theory but I will think on it for a minute.

  2. Loser66
    • one year ago
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    I post the wrong question, now I correct it. Surely the previous one is easy. :)

  3. Empty
    • one year ago
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    2*3, 3*5, 2*5 ?

  4. zzr0ck3r
    • one year ago
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    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 \(2\).

  5. Empty
    • one year ago
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    pq, qr, rp That's a fun more general case. But not like super best.

  6. zzr0ck3r
    • one year ago
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    ahh I c. Yeah, what @Empty said

  7. Loser66
    • one year ago
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    oh oh.... they are integers!! not primes. GGGGGGGGGGGGot it. :)

  8. Loser66
    • one year ago
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    @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

  9. Empty
    • one year ago
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    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!!

  10. Loser66
    • one year ago
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    oh yeah. I am sorry. I should take a snap. :(

  11. zzr0ck3r
    • one year ago
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    lol

  12. Empty
    • one year ago
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    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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