A circuit consists of a resistance R connected to n  similar cells.  If the current in the circuit is the same whether the cells are connected in series or in parallel then the internal resistance r of each cell is given by

r = R 

$\text{ If n cells are connected in series then } I = \frac{nE}{R + nr}$

$\text{If n cells are connected in parallel } I'= \frac{E}{R + r/n}$

$I = I'$

$\frac{nE}{R + nr} = \frac{E}{R + r/n}$ 

$nR + r = R + nr$

$R = r$