How many of the 343 smallest positive integers written in base 7 use 4 or 5 (or both) as a digit?
+1253 \(343_{10}=1000_7\)
So the 4 or 5 must be in the 49's, 7's or 1's place.
There are \(49\times 2=98\) , \(7\times 2=14\) , and \(1\times 2=2\), so \(98+2+14=114\).
There are 114 of those integers.
You are very welcome!
:P
