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 December 30th, 2018, 02:26 PM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 636 Thanks: 91 Number of solutions Find the number of pairs $\displaystyle (n_1,n_2)$ that satisfies the equation below: $\displaystyle n_1 + n_2 = x\; \;$ where $\displaystyle n_1 ,n_2 ,x \in \mathbb{N}$ Last edited by idontknow; December 30th, 2018 at 02:32 PM. December 30th, 2018, 03:16 PM   #2
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Quote:
 Originally Posted by idontknow Find the number of pairs $\displaystyle (n_1,n_2)$ that satisfies the equation below: $\displaystyle n_1 + n_2 = x\; \;$ where $\displaystyle n_1 ,n_2 ,x \in \mathbb{N}$
Let's rephrase the problem statement a bit.
$\displaystyle n_1 + n_2 = x$

$\displaystyle n_2 = x - n_1$

So
$\displaystyle n_1 = 1$, $\displaystyle n_2 = x - 1$.

$\displaystyle n_1 = 2$, $\displaystyle n_2 = x - 2$.

And now it's a counting problem. How many values can $\displaystyle n_1$ take on?

-Dan December 31st, 2018, 02:37 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 636 Thanks: 91 It is seen that $\displaystyle x\geq 2$ Number of pairs is dependent on $\displaystyle x$ Example , $\displaystyle x=10^{10}$ December 31st, 2018, 12:17 PM   #4
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Quote:
 Originally Posted by idontknow It is seen that $\displaystyle x\geq 2$ Number of pairs is dependent on $\displaystyle x$ Example , $\displaystyle x=10^{10}$
Yes. Though I'm not going to try to list all that with your x value!

-Dan December 31st, 2018, 04:57 PM #5 Senior Member   Joined: Dec 2015 From: somewhere Posts: 636 Thanks: 91 What i got is $\displaystyle f(x)=x-1$ Where f(x) is the number of pairs December 31st, 2018, 06:00 PM   #6
Math Team

Joined: May 2013
From: The Astral plane

Posts: 2,270
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Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 Originally Posted by idontknow What i got is $\displaystyle f(x)=x-1$ Where f(x) is the number of pairs
Yes.

-Dan Tags number, solutions 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 Nathalia Trigonometry 3 September 29th, 2016 10:22 PM taznick Calculus 1 June 11th, 2015 05:26 AM ishaanmj007 Algebra 4 May 16th, 2015 04:38 PM Bolt Algebra 7 July 31st, 2011 07:06 AM earth Math Events 3 July 8th, 2009 09:14 PM

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