Prob in Diophantine

[rakeen]

In moon bhaiya's tutorial(found on KMC)(named Introduction to number theory_KMC_by TAM) there's a section named Diophantine's Equation. There he stated that we can find the result of x and y by this formula:


$x$ $=$ $x_o$ $+$ $\frac{bn}{d}$ and so the y goes: $y$ $=$ $y_o$ $-$ $\frac{an}{d}$


here $x_o$ and $y_o$ is the number which denotes the equations result. But there are lots of result for an equation. If I calculate with other result, for i.e.

$2x$ $+$ $3x$ $=$ $1$


here if I take ($x_o$,$y_o$)=(-1,1) then we get (x,y)=(3n-1,1-2n)

here n denotes 'purno sonkha'

but if we place 100 instead of n then the equation doesn't match.

[Moon]

You should use calculator before you post, when you are not sure about something.
$(x_{100},y_{100})=(299,-199)$ So, $2.299 - 3.199 = 1$

BTW your equation should be $2x+3y=1$ not $2x+3x=1$.

[rakeen]

Moon said:'BTW your equation should be 2x+3y=1 not 2x+3x=1 .'
typo!

and that time I placed 100 in the main(2x+3y=1) equation. Beside that every thing iz okay~ thnx again*