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The search turned on up a 1981 paper by John S.Lew (in the Unsolved problems section)

which discusses related problems, and ends up stating this one. In The author's terminologyproblems are:

  • Problem A. Classify bijections $\mathbb N\times\mathbb N \to \mathbb N$.
  • Problem B. Classify bijections $\mathbb Z\times\mathbb Z \to \mathbb Z$.
  • Problem C. Classify surjections $\mathbb Z\times\mathbb Z \to \mathbb N$.

His main conjecture is that the only solutions to A is are Cantor's $x+ \frac12(x+y-1)(x+y-2)$, which apparently goes to the time of Polya. Lew appears to state states C independently from empirical observations.
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The search turned on a 1981 paper by John S.Lew , (in the Unsolved problems section)

which discusses related problems, and ends stating this one. In author's terminology:

  • Problem A. Classify bijections $\mathbb N\times\mathbb N \to \mathbb N$.
  • Problem B. Classify bijections $\mathbb Z\times\mathbb Z \to \mathbb Z$.
  • Problem C. Classify surjections $\mathbb Z\times\mathbb Z \to \mathbb N$.

His main conjecture is that the only solutions to A is Cantor's $x+ \frac12(x+y-1)(x+y-2)$, which apparently goes to the time of Polya. Lew appears to state C independently from empirical observations.
show/hide this revision's text 1

The search turned on a 1981 paper by John S.Lew,

which discusses related problems, and ends stating this one. In author's terminology:

  • Problem A. Classify bijections $\mathbb N\times\mathbb N \to \mathbb N$.
  • Problem B. Classify bijections $\mathbb Z\times\mathbb Z \to \mathbb Z$.
  • Problem C. Classify surjections $\mathbb Z\times\mathbb Z \to \mathbb N$.

His main conjecture is that the only solutions to A is Cantor's $x+ \frac12(x+y-1)(x+y-2)$, which apparently goes to the time of Polya. Lew appears to state C independently from empirical observations.