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Statement

The properties are those of the paper's definitions.

Question (Section 5, p. 12, quoted). "It is known that the sequence of squares $\{n^2\}$ does not have property $AP$. Does it have preoprty [sic] $QP,CP$, or $C$?"

By Theorem 1, $QP\Rightarrow CP\Rightarrow C$, so the three questions are nested: a yes for QP gives a yes for CP and for C, and a no for C gives a no for CP and for QP.

Source. Brown, T. C., Erdős, P. and Freedman, A. R., Quasi-progressions and descending waves, J. Combin. Theory Ser. A 53 (1990), no. 1, 81--95, doi:10.1016/0097-3165(90)90021-N, read in the authors' copy identified on the source card, whose pages are numbered 1 to 13: the question on p. 12.

Read depth. Claims checked: the question was read on the print's page. Nothing here is independently reviewed.

Proof pointer

An open question as posed; the paper gives no argument.

Dependencies

None.

Bears on

• Problem 782: the problem's two questions, whether the squares contain arbitrarily long quasi-progressions of bounded diameter and whether they contain arbitrarily large cubes, are the paper's questions for QP and for C. The paper poses them and proves nothing about them.