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: 3

2006 Singapore Senior Math Olympiad, 1
Tags: mutliple , divide , divisible , prime , number theory
Let $a, d$ be integers such that $a,a + d, a+ 2d$ are all prime numbers larger than $3$. Prove that $d$ is a multiple of $6$.

2013 Junior Balkan Team Selection Tests - Romania, 2
Tags: number theory , sum of digits , digit , mutliple
Call the number $\overline{a_1a_2... a_m}$ ($a_1 \ne 0,a_m \ne 0$) the reverse of the number $\overline{a_m...a_2a_1}$. Prove that the sum between a number $n$ and its reverse is a multiple of $81$ if and only if the sum of the digits of $n$ is a multiple of $81$.

2007 May Olympiad, 1
Tags: number theory , mutliple
Determine the largest natural number that has all its digits different and is a multiple of $5$, $8$ and $11$.