David Hockney the Order of Merit, an honour restricted to 24 members at any one time for their contributions to the arts and sciences. He was a Distinguished Honoree of the National Arts Association, Los Angeles, in 1991 and received the First Annual Award of Achievement from the Archives of American Art, Los Angeles, in 1993. He was appointed to the Board of Trustees of the American Associates of the Royal Academy Trust, New York in 1992 and was given a Foreign Honorary Membership to the American Academy of Arts and Sciences, Cambridge, Massachusetts in 1997. In 2003, Hockney was awarded the
Restricted sumset Restricted sumset In additive number theory and combinatorics, a restricted sumset has the form where formula_2 are finite nonempty subsets of a field "F" and formula_3 is a polynomial over "F". When formula_4, "S" is the usual sumset formula_5 which is denoted by "nA" if formula_6; when "S" is written as formula_8 which is denoted by formula_9 if formula_6. Note that |"S"| > 0 if and only if there exist formula_11 with formula_12. The Cauchy–Davenport theorem named after Augustin Louis Cauchy and Harold Davenport asserts that for any prime "p" and nonempty subsets "A" and "B" of the prime order