Number theory · Divisibility · Powers of three · P adic valuation · Iterative process
Jure wrote all the natural numbers from \(1\) to \(2015\) on a board. Urska then went through the numbers on the board from the smallest to the largest and rubbed out every one that was not divisible by \(3\). Going through the numbers still on the board, again from the smallest to the largest, she then rubbed out every one that was not divisible by \(3^2\). From those remaining she next rubbed out, again in increasing order, every number not divisible by \(3^3\), and she continued in this way. Which number did Urska rub out last?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2015, 1. letnik, category A, problem B2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source