please solve the following "Diophantus equation "
(I know how to solve it , may be your solution is better ,please have a try ,many thanks !)
mn+nr+mr=2(m+n+r)
where m,n,r are all positive integers
Ans:there are 7 combinations of (m,n,r)
please solve the following "Diophantus equation "
(I know how to solve it , may be your solution is better ,please have a try ,many thanks !)
mn+nr+mr=2(m+n+r)
where m,n,r are all positive integers
Ans:there are 7 combinations of (m,n,r)
Move everything to one side and regroup:
This can be rewritten as
I'll let a = m-1, b = n-1, c = r-1 where a,b,c are non-negative integers, that is .
Here, either (a,b,c) = (1,1,1) or (0,1,3) (up to re-arranging). This leaves 1! + 3! = 7 solutions.