calculus + co-ordinate

\large [x].[y]=x+y\,\rightarrow all\,non\,integer\,sol.\,lies\,on\,exactly\,2\,lines\,find\,them.

3 Answers

62
Lokesh Verma ·

{x} + {y} is either 0 or 1

Now can you try?

1
Hodge Conjecture ·

sir how {x} + {y} =0 /1

sir am doing it in this way.....

let x= I1+ f1 nd y=I2+ f2

so we can write ...

[ I1+ f1].[I2+ f2]= f1 +I2+ f2 + I1

i.e ... I1 . I2 = I1 + I2 + f1 + f2

sir, how to proceed from here..............?

62
Lokesh Verma ·

that is fairly correct..

now observe that LHS is an integer..

so RHS has to be an integer.. so RHS has to be either 0 or 1..

now can you proceed?

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