- #1
Euge
Gold Member
MHB
POTW Director
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- 244
Here is this week's POTW:
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For $n$ a positive integer, let $\phi(n)$ be the number of positive integers not exceeding $n$ and coprime to $n$. Show that every composite number $n \equiv 1\pmod{\phi(n)}$ has at least three distinct prime divisors. (In fact, $n$ would have at least four distinct prime divisors. You can prove this harder result if you like.)
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Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!
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For $n$ a positive integer, let $\phi(n)$ be the number of positive integers not exceeding $n$ and coprime to $n$. Show that every composite number $n \equiv 1\pmod{\phi(n)}$ has at least three distinct prime divisors. (In fact, $n$ would have at least four distinct prime divisors. You can prove this harder result if you like.)
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Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!