mlb>In fact, recalling this, I'd hoped to retrieve some collective memories! acw>> Gosper showed me an absurdly intricate _analytic_ proof of this, and
bewailed the lack of a _combinatorial_ proof;
Here are my memories. Unfortunately, the TeX sources appear to to have been abandoned at Xerox PARC. Shortly after the announcement of the factorization of 2^2^2^3+1, I sent a(n unrelated) letter to the the usual gang of maniacs (Dick Askey, George Andrews, George Gasper (I think), Rich&Hilarie, etc.) that began: "Dear Thai food lovers and Rich," answering Hilarie's challenge to find a bijection between the *complements* of the odd partitions and distinct partitions. I.e., pair the not-all-differents with the not-all-odds. A very young Peter Weyhrauch and I came up with one, and then a PARC coworker, Ted Kaehler, came up with a different one! I then found a generalization of the theorem to residue classes mod k, of which #(some evens) = #(some duplicates) was the case k=2. This led to a nonobvious generating function identity. It would be nice to locate a hardcopy of that letter. --rwg