this one is from Gelfand's book "Algebra".
Problem 204. Is it possible that numbers $\frac{1}{2}$, $\frac{1}{3}$, and $\frac{1}{5}$ are (not necessarily adjacent) terms of the same arithmetic progression?
Is there a method to show if they're from same progression? or should I just try different differences?
All that came to my mind was to write system of equations: $\left\{\begin{array}\frac{1}{2}-nd=\frac{1}{3}\\\frac{1}{3}-kd=\frac{1}{5}\end{array}\right.$ But it can't be solved for $d$ (difference).
By the way, answer is $d=-\frac{1}{30}$, which is $-2*5*3$, so maybe the difference depends on denominators of progression?