/sci/ - Science & Math

>>1112198

I'll show my demonstration.

5 = 2*2 + 1
1 = 5 - 2*2
10000 = 5*10000 - 2*20000

We have (-20000,10000) as a solution couple.

We have now;

2x + 5y = 10000
2*-20000 + 5*10000 = 10000

So,

2x + 5y - (2*-20000 + 5*10000) = 0

2x + 5y + 2*20000 - 5*10000 = 0

2 (x+20000) - 5(-y+10000) = 0

2 (x+20000) = 5 (-y+10000)

We have:

2 | 5 (-y+10000) & 2^5 = 1

So: 2 | -y+10000

-y+10000 = 2q
>y = 10000-2q

And; 5 | 2 (x+20000) & 5^2 = 1

So; 5 | (x+20000)

x+20000 = 5q

>x = 5q - 20000


So.

(x,y) = (5q-20000,10000-2q)

FUCK YEAH.