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mathmath333

  • one year ago

Find the number of integer solutions.

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} 5x+8y=1\hspace{.33em}\\~\\ x<100,\ y<100 \end{align}}\)

  2. anonymous
    • one year ago
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    @satellite73 @ganeshie8

  3. ganeshie8
    • one year ago
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    By inspection \((-3,2)\) is one solution, and the null solution is \((-8t,5t)\) Therefore all the solutions are given by \[(-3,2)+(-8t,5t)\] which is same as \[(-3-8t,~2+5t)\] so we need to find the number of \(t\) values such that \(-3-8t\lt 100\) and \(2+5t\lt 100\)

  4. anonymous
    • one year ago
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    Hey, ganeshie, what branch of math is this? Number theory or something? Havent done a problem like it, so curious xD

  5. ganeshie8
    • one year ago
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    yes.. linear diophantine equations... here is a much simpler problem http://math.stackexchange.com/questions/897356/how-to-find-natural-solutions-of-an-equation/897369#897369

  6. anonymous
    • one year ago
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    Okay, heard of diophantine before. Ill take a look, thanks :)

  7. ganeshie8
    • one year ago
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    np :)

  8. mathmath333
    • one year ago
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    is the answer \(31\) @ganeshie8

  9. ganeshie8
    • one year ago
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    \(-3-8t\lt 100 \implies t \gt -12.87\) \(2+5t\lt 100 \implies t \lt 19.6\) so \(-12.87 \lt t\lt 19.6\)

  10. ganeshie8
    • one year ago
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    that gives 32 solutions right ?

  11. mathmath333
    • one year ago
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    how did u count that

  12. ganeshie8
    • one year ago
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    -12.87 to 19.6 12 negative integers 19 positive integers and a zero

  13. mathmath333
    • one year ago
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    ok i forgot 0

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