Motivated by a mathematical logic problem, J.R. Buchi proposed the
following problem in the early 1970’s.
Problem (B¨uchi’s problem). B2(Z). Does there exist a positive integer M
such that any sequence of M integer squares, with second difference constant
equal to the constant sequence (2)n, is of the form
((x + n)2)n, where n =1, . . . ,M, for some integer x?