3 integer unknowns and 1 equation

Asked Aug 19 '21 at 23:39

Active Aug 19 '21 at 23:39

Viewed 57 times

All numbers are integers and none equate to 0.

$$ 4=\frac{a}{b+c}+ \frac{b}{a+c} + \frac{c}{b+a} $$

My friend made this question, I tried to solve it for 2 hours and then he told me that I needed to use cryptology. I want to see how questions like these are solved. Answers: -1, 4, 11

asked Aug 19 '21 at 23:39

John Smith

I get $11, 9$, and $-5$. – David G. Stork Aug 19 '21 at 23:56
1

"Use cryptology" is not a meaningful hint as far as I can tell. – Greg Martin Aug 20 '21 at 01:43
Note that you need to add a requirement that they are not divisible by same number. – Moti Aug 20 '21 at 05:13
It's an interesting maths problem if the constraint $a,b,c \gt 0$ is added, which is the usual form of the question – Arthur Vause Aug 20 '21 at 07:44
1

See this post: https://math.stackexchange.com/questions/402537/find-integer-in-the-form-fracabc-fracbca-fraccab – Arthur Vause Aug 20 '21 at 07:45
I think by "crypto" your friend might have meant elliptic curves – Arthur Vause Aug 20 '21 at 07:53
As an aside, I once posted the equation on facebook using fruit, as a counter to all the tedious simultaneous equation puzzles that were appearing on social media at the time.
https://drive.google.com/file/d/1wa744g6K5HOIsiaI3TX3jOpv9y9pKoYX/view?usp=sharing
– Arthur Vause Aug 20 '21 at 09:06
Thanks @ArthurVause – John Smith Aug 20 '21 at 12:07
5

Does this answer your question? Find integer in the form: $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$ – kelalaka Aug 20 '21 at 19:04

3 integer unknowns and 1 equation

0 Answers0