Originally Posted by
watzer Hi! I'm stuck!
How to prove that a equation x + y = n always have a positive solution(x,y >= 0) when n > z?
What is z??
"a Linear Diophantine equation"
(Ex: 69x + 39y = n, when n > 20)
This is false: any solution to this equation will have x or y negative if , for example, n = 21
Tonio
My steps have been:
Solve the equation as u solve diofantic equations:
so u get:
Ex:
x + y = 1 (in my case GCD(x,y) were one)
then i did multiply all solutions with the value EX: 21,22,23,24,25 ( if n > 20 )
and i got diffrent x,y values on all five wich had all one value of K were X,Y where positive.
(ex:x = -110-49k, y = 155 + 69k)
and all solutions over n > z had atleast one solution wich both x and y were positive.
And then i got a pattern similar to this
Ex:
n 21---22----23---24----25
X 50---52----54---56----58
Y 100--105--110--115--120
K 2-----2-----3-----3------4
But have no idea how to prove it with induction.
Is it posible to prove X then prove Y and by that K is proven to consist and always have a solution ?