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Find the number of positive integers less than 1000 that can be expressed as the difference of two integral powers of \(3\).

 Jun 13, 2022
 #1
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$your \ face \ HAH \ LOL \ GET \ IT$

 Jun 14, 2022
 #2
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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.

 Jun 14, 2022

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