A short WZ-style proof of Abel's identity.

Ekhad, Shalosh B.; Majewicz, John E.

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A bijective proof of $f_{n + 4} + f_{1} + 2 f_{2} + \dots + n f_{n} = (n + 1) f_{n + 2} + 3$ .

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We study the decidability of the following problem: given $p$ affine functions $f_{1}, ..., f_{p}$ over $ℕ^{k}$ and two vectors $v_{1}, v_{2} \in ℕ^{k}$ , is $v_{2}$ reachable from $v_{1}$ by successive iterations of $f_{1}, ..., f_{p}$ (in this given order)? We show that this question is decidable for $p = 1, 2$ and undecidable for some fixed $p$ .