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 Pre-Calculus Pre-Calculus Math Forum

 February 3rd, 2019, 11:57 PM #1 Newbie   Joined: Feb 2019 From: home Posts: 5 Thanks: 0 mathematics help Problem 2.2 Find all functions $f$ : $\mathbb{N}\to \mathbb{N}$ which satisfy (a) $f(2) = 2$; (b) $f(mn) = f(m)f(n)$ for all $m,n$ in $\mathbb{N}$ satisfying the condition $\gcd(m,n) = 1$; (c) $f(m) < f(n)$ whenever $m < n$. This is a question from my book. I attempted it as and The book uses induction to solve (though I couldn't understood that). Have I correctly attempted it? And is it possible to include induction anywhere? Thank you. Last edited by skipjack; February 4th, 2019 at 12:31 AM. February 4th, 2019, 12:44 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,973 Thanks: 2224 Condition (b) doesn't use the wording "only when". What exactly do you find hard to understand in relation to mathematical induction? February 4th, 2019, 02:18 AM #3 Newbie   Joined: Feb 2019 From: home Posts: 5 Thanks: 0 Condition (b) in question implicitly telling 'only when'. it writes: f(mn)=f(n)f(m) where m,n satisfying the condition gcd(m,n)=1 Suppose I want to check my answer through induction, then how do I? Can you provide steps? Last edited by skipjack; February 4th, 2019 at 02:58 AM. February 4th, 2019, 03:07 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,973 Thanks: 2224 The problem's wording isn't intended to mean "only when". The problem leaves it to you to determine whether $f(mn) = f(m)f(n)$ is also true when the given condition isn't satisfied. Mathematical induction is a proof technique. Tags function, mathematics 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 Navina Calculus 3 September 27th, 2014 05:48 AM zaidalyafey New Users 12 February 17th, 2013 05:55 PM r-soy Calculus 2 February 8th, 2013 10:16 AM Mai Abstract Algebra 6 June 6th, 2010 01:39 AM Mai Number Theory 0 December 31st, 1969 04:00 PM

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