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: 6

2013 India PRMO, 18
Tags: sum , maximum , consecutive integers , algebra
What is the maximum possible value of $k$ for which $2013$ can be written as a sum of $k$ consecutive positive integers?

2017 Hanoi Open Mathematics Competitions, 12
Tags: prime , consecutive integers , number theory
Does there exist a sequence of $2017$ consecutive integers which contains exactly $17$ primes?

2014 JHMMC 7 Contest, 14
Tags: consecutive integers
$11$ consecutive integers sum to $1331$. What is the largest of the $11$ integers?

Estonia Open Junior - geometry, 2001.2.2
Tags: consecutive integers , perpendicular , geometry
In a triangle $ABC$, the lengths of the sides are consecutive integers and median drawn from $A$ is perpendicular to the bisector drawn from $B$. Find the lengths of the sides of triangle $ABC$.

II Soros Olympiad 1995 - 96 (Russia), 11.7
Tags: summation , consecutive integers , number theory
Find three consecutive natural numbers, each of which is divisible by the square of the sum of its digits. Prove that there are no five such numbers in a row.

2009 Puerto Rico Team Selection Test, 2
Tags: combinatorics , consecutive integers , sum
In each box of a $ 1 \times 2009$ grid, we place either a $ 0$ or a $ 1$, such that the sum of any $ 90$ consecutive boxes is $ 65$. Determine all possible values of the sum of the $ 2009$ boxes in the grid.