Thread: An integer equation View Single Post
2019-01-05, 00:25   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by enzocreti Consider the equation a*(2*a^2+2*b^2+c^2+1)=(2*a^3+2*b^3+c^3+1) with a,b,c positive integers. Are the only solutions to that equation a=1, b=1, c=1 and a=5, b=4 and c=6?
multiplying each side through gives:

$2a^3+2ab^2+ac^2+a=2a^3+2b^3+c^3+1$

which then cancels down to:

$2ab^2+ac^2+a=2b^3+c^3+1$

which with a=b=c=1 goes to:

$2b^3+c^3+1=2b^3+c^3+1$

So no, there are multiple solutions. That being said, you should be able to work this out on your own, before you get taken seriously. okay sorry didn't see you listed a=c=b=1 . You could try algebraic relations between variables. then you can use them to go to univariate polynomials and apply polynomial remainder theorem.

Last fiddled with by science_man_88 on 2019-01-05 at 00:45