This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 127

1998 Czech And Slovak Olympiad IIIA, 4
Tags: number theory , max , power of 3
For each date of year $1998$, we calculate day$^{month}$ −year and determine the greatest power of $3$ that divides it. For example, for April $21$ we get $21^4 - 1998 =192483 = 3^3 \cdot 7129$, which is divisible by $3^3$ and not by $3^4$ . Find all dates for which this power of $3$ is the greatest.

2018 Hanoi Open Mathematics Competitions, 7
Tags: power of 2 , sum , max , number theory
Some distinct positive integers were written on a blackboard such that the sum of any two integers is a power of $2$. What is the maximal possible number written on the blackboard?