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.
Prob in Diophantine
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Re: Prob in Diophantine
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 $2x+3x=1$.
$(x_{100},y_{100})=(299,-199)$ So, $2.299 - 3.199 = 1$
BTW your equation should be $2x+3y=1$ not $2x+3x=1$.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: Prob in Diophantine
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*
typo!
and that time I placed 100 in the main(2x+3y=1) equation. Beside that every thing iz okay~ thnx again*
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