Find the number of positive integers less than 1000 that can be expressed as the difference of two integral powers of \(3\).
if we make a list of all numbers which are differences of powers of three, all will be different if we insist that the powers are different. The number of differences with minuend ( a number from which another is subtracted), 3^n is n. The last minuend leaving a difference less than 1000 is 3^6. 1+2+3+4+5+6=21
Note: if you include "0", then you have a total of 22.