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MathNet 2010 — Part 01 Question 64

Math Olympiad Vault · MathNet 2010 — Part 01

Question 64

Find all coprime positive integers $a$ and $b$ with the following property: There exists positive integer $N$ such that any positive integer, greater than $N$, has the form $\sum a^i b^j$, where $i$ and $j$ are non-negative integers and none of the summands divides any other.