Problem
NT-B1-M10-P009 Bases with Divisibility by \(5\)
#9
★★☆☆☆ Level 2 of 5
Find all bases \(b>4\) for which \((34)_b\) is divisible by \(5\).
Translate \((34)_b\) into \(3b+4\).
We need \(3b+4\equiv0\pmod5\), so \(3b\equiv1\pmod5\). The inverse of \(3\) modulo \(5\) is \(2\), hence \(b\equiv2\pmod5\). With \(b>4\), \(b=5t+2\), \(t\ge1\).
Connects base notation with linear congruences.