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: 28

2017 CCA Math Bonanza, I3
Tags: algebra , factorization , sum of cubes
A sequence starts with $2017$ as its first term and each subsequent term is the sum of cubes of the digits in the previous number. What is the $2017$th term of this sequence? [i]2017 CCA Math Bonanza Individual Round #3[/i]

2021 German National Olympiad, 3
Tags: digit , sum of cubes , combinatorics , algebra
For a fixed $k$ with $4 \le k \le 9$ consider the set of all positive integers with $k$ decimal digits such that each of the digits from $1$ to $k$ occurs exactly once. Show that it is possible to partition this set into two disjoint subsets such that the sum of the cubes of the numbers in the first set is equal to the sum of the cubes in the second set.

2009 Stanford Mathematics Tournament, 2
Tags: geometry , 3d geometry , algebra , factorization , sum of cubes
Factor completely the expression $(a-b)^3+(b-c)^3+(c-a)^3$