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mathmath333
 one year ago
Find the number of integer solutions.
mathmath333
 one year ago
Find the number of integer solutions.

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} 5x+8y=1\hspace{.33em}\\~\\ x<100,\ y<100 \end{align}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@satellite73 @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5By 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 \[(38t,~2+5t)\] so we need to find the number of \(t\) values such that \(38t\lt 100\) and \(2+5t\lt 100\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hey, ganeshie, what branch of math is this? Number theory or something? Havent done a problem like it, so curious xD

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5yes.. linear diophantine equations... here is a much simpler problem http://math.stackexchange.com/questions/897356/howtofindnaturalsolutionsofanequation/897369#897369

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, heard of diophantine before. Ill take a look, thanks :)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1is the answer \(31\) @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5\(38t\lt 100 \implies t \gt 12.87\) \(2+5t\lt 100 \implies t \lt 19.6\) so \(12.87 \lt t\lt 19.6\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5that gives 32 solutions right ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1how did u count that

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.512.87 to 19.6 12 negative integers 19 positive integers and a zero
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