Number Theory-Symmetric Divisibility Conditions

by XmL, May 28, 2014, 5:55 AM

Today on Brilliant a problem like this caught my eyes:

Find all primes $p,q,r$ such that $p\mid qr-1, q\mid pr-1, r\mid pq-1$.

As mentioned in the title, this is an example of a problem with "Symmetric Divisibility", and it is also one of my favorite explorative topics in number thoery(although I'm not sure if there's an actually devotion to this topic).

Solution

Note to solution

Another "Symmetric Divisibility" I like is $x\mid y^2+1, y\mid x^2+1$
This post has been edited 2 times. Last edited by XmL, Aug 12, 2014, 11:18 PM

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Still an immature proof writer :)

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  • Good blog! I hope to see more posts here!

    by WizardMath, Feb 3, 2018, 6:57 PM

  • Thanks Harry Potter :D

    by XmL, Jul 30, 2014, 10:47 PM

  • Hey dude. Nice blog. I like your work.

    by gamjawon, Jul 30, 2014, 7:43 AM

  • Thanks...although most of the posts here won't be about geometry...rightnow I'm trying to improve my skills in other areas such as number theory and combo.

    by XmL, Jun 5, 2014, 1:11 AM

  • Hi Geometer,,nice blog..:D

    by vanu1996, Jun 4, 2014, 1:27 PM

  • Check your private massage :)

    by zabihpourmahdi, Jan 11, 2013, 5:34 PM

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