A circuit contains a 1V cell and some identical 1 ohm resistors. A voltage of a/b, where $a\leq b$, is to be made across a voltmeter using the minimum number of resistors in the circuit. The voltage across part of a circuit = resistance across that part/total resistance. The total resistance of n resistors in parallel = 1/n, and resistance of n in series = n.
Pretend that there is no resistance in the wires, and that the voltmeter does not draw any current. $a,b,m,n,p\subset N$
Denote the minimum number of resistors required f(a,b).
I have noticed that $f(mp,mn+1)\leq n+m$ if $m