Problem 5

Is it possible to choose

1983

distinct positive integers, all less than or equal to

10^5

, no three of which are consecutive terms of an arithmetic progression? Justify your answer.

Step 4 of 4: Finish the construction

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\{a_1,a_2,\ldots,a_{1983}\}\text{ works}

Detailed analysis

The binary-to-ternary digit map is injective, so the $a_n$ are distinct positive integers. Step 2 excludes every three-term arithmetic progression, and Step 3 gives the size bound. Thus the answer is yes.