Claims

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1965_01_01_sarkozy_szemeredi: The Satz of Sárközy and Szemerédi: for n distinct positive reals and large n, no value is a subset sum in more than (1 + epsilon)(8/sqrt pi) 2^n/n^1.5 ways; the affirmative answer to the first question of Problem 362.

1977_09_01_halasz: Halász's Theorem 2: if for every unit vector e at least delta n of the n 1-separated vectors in d-space have |(a_k, e)| at least 1, at most c 2^n n^(-1-d/2) signed sums lie in a unit ball; d = 2 answers the second question.

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