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MathNet 2022-part-03 — 197 problems (EN–VI) Question 174

Math Olympiad Vault · MathNet 2022-part-03 — 197 problems (EN–VI)

Question 174

We construct a sequence of numbers starting with $2022$ and $21$. Each next number in the sequence is equal to the positive difference of the two previous numbers. So the third and fourth number in the sequence are $2001$ and $1980$.
At which place in the sequence do we find the number $0$ for the first time?