If $a$ and $b$ both are positive integer,then prove that the given equation has no solution:
$\dfrac {1}{a^2}+\dfrac {1}{ab}+\dfrac {1}{b^2}=1$
Unsolvable equation
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Re: Unsolvable equation
Multiply the whole equation by $a^2b^2$.The equation turns to $a^2+ab+b^2$=$a^2b^2$.Add $ab$ to both sides and so $(a+b)^2-(ab)^2=ab$.Observe that $a+b$>$ab$.Notice that $(ab+1)^2-(ab)^2$=$2ab+1$>$ab$.The rest is trivial.