My Math Forum Euler's totient function equation

 Number Theory Number Theory Math Forum

 April 9th, 2018, 06:53 AM #1 Newbie   Joined: May 2017 From: Moscow Posts: 6 Thanks: 0 Euler's totient function equation $\displaystyle \varphi(8x)=96$ How do I find x?
 April 9th, 2018, 07:57 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,059 Thanks: 1619 Does x have to be a natural number?
 April 9th, 2018, 08:10 AM #3 Newbie   Joined: May 2017 From: Moscow Posts: 6 Thanks: 0 Yes, sorry forgot to specify that.
 April 9th, 2018, 11:35 AM #4 Senior Member   Joined: Sep 2016 From: USA Posts: 383 Thanks: 207 Math Focus: Dynamical systems, analytic function theory, numerics Consider cases for divisibility of $x$ by $2^k$ for $k = 0,1,2...$ and use the fact that $\varphi$ is multiplicative for coprime factors. Example: Suppose $x$ is odd (i.e.\ $k= 0$), then gcd$(8,x) = 1$ so you must have $\varphi(8x) = \varphi( 8 ) \varphi(x) = 96 \implies \varphi(x) = 24$ Solve this by considering the decomposition of $x$ into prime powers and apply the multiplicative property once again. Repeat for the case that $x = 2^kn$ for $n$ odd with increasing $k$ and it won't take long to conclude all possible values of $k$. Do you see why? Thanks from topsquark, Adam Ledger and cjem

 Tags equation, euler, function, totient

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post milind Number Theory 1 July 25th, 2014 05:27 AM milind Number Theory 2 July 25th, 2014 05:15 AM matqkks Number Theory 1 October 26th, 2013 09:12 AM maxgeo Number Theory 5 April 20th, 2013 06:47 AM fucktor Number Theory 3 April 13th, 2009 11:34 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top