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Find integral solution to the eqation [x][y]=x+y. show that all non-integral solution lie on exactly two lines. determine these lines. Thanks

 
Find   integral solution to the eqation
[x][y]=x+y. show that all  non-integral solution lie on exactly two lines. determine these lines.

Thanks

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1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
8 years ago
[x]=x- frac(x)= x-x’
[y]=y-frac(y) =y-y\

[x][y]=(x- frac(x))(y-frac(y) )
xy- xy’- x’y-x’y’ = x+y
xy- xy’- x’y-x’y’ –x- y is equation of pair of line, hence proved




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