Find all positive integers n such that there are $$k\geq$$ 2 positive rational numbers a1, a2, ............... , ak
satisfying $$a_1+a_2+................+a_k$$=$$a_1a_2...............a_k$$ = n.
An Interesting problem
Re: An Interesting problem
as much as I know $\pm 6\ and 0$ satisfy it!! haven't really tried it yet! 
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"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Re: An Interesting problem
I'd like to draw everyone's attention to the fact that the topics of many posts are not effective. Without using a proper topic, you actually break the rule number 1 of this forum.
viewtopic.php?f=9&t=6
For example, the title of this post is "An interesting problem". You can see below that there is already another topic with the same name! You could use something like find when sum is equal to product...I just want to request everyone to be careful about this thing. This is for our own good.
viewtopic.php?f=9&t=6
For example, the title of this post is "An interesting problem". You can see below that there is already another topic with the same name! You could use something like find when sum is equal to product...I just want to request everyone to be careful about this thing. This is for our own good.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
-
Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: An Interesting problem
there are no solutions because the sum of $$n$$ integers $$\geq2$$ can not be equal to both their product and $$n$$.
If 1 of the conditions are removed,there might be a solution
If 1 of the conditions are removed,there might be a solution
বড় ভালবাসি তোমায়,মা
Re: An Interesting problem
@ tahmid, If $k=3, a_1=1, a_2=2, a_3=3$ then $n=6=1\times 2\times 3=1+2+3$
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Re: An Interesting problem
Moon bhaia, How to change the name? I can't see any options here?Moon wrote:I'd like to draw everyone's attention to the fact that the topics of many posts are not effective. Without using a proper topic, you actually break the rule number 1 of this forum.
viewtopic.php?f=9&t=6
For example, the title of this post is "An interesting problem". You can see below that there is already another topic with the same name! You could use something like find when sum is equal to product...I just want to request everyone to be careful about this thing. This is for our own good.