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 Number Theory Number Theory Math Forum

 December 28th, 2018, 11:58 PM #11 Senior Member   Joined: Oct 2009 Posts: 850 Thanks: 325 The first thing you'd need to prove is that $\varphi(n)$ is not $<5$ infinitely many times. So you'd need to prove there actually IS an N such that for $n\geq N$, $\varphi(n)\geq 5$. Use the prime decompositions for that, and the formula of $\varphi$ on such decompositions. When proving this, you'll be able to constructively find a value of $N$. Then it is just a matter of checking all values from $1$ to $N$. December 29th, 2018, 09:38 PM #12 Newbie   Joined: Dec 2018 From: Euclidean Plane Posts: 7 Thanks: 3 Here's a start: For any positive integer $n$, if $n$ is divisible by a prime factor $p \ge 7$, then $\phi(n)$ contains $p-1 \ge 6$ as a factor. So any number $n$ with $\phi(n) < 5$ can only have 2, 3, and 5 as prime factors. Tags euiler, euler Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post MMath Elementary Math 11 May 27th, 2016 12:01 AM FalkirkMathFan Calculus 1 November 5th, 2011 12:57 AM FalkirkMathFan Real Analysis 0 November 4th, 2011 04:08 AM FalkirkMathFan Calculus 0 November 3rd, 2011 04:52 PM brangelito Number Theory 18 August 9th, 2010 11:58 PM

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