A variant of a statement by this man that adds positive integer coefficients is named after S. S. Pillai. Preda Mihailescu used cyclotomic polynomials to prove a conjecture named for this man, (-5[1])which asserts that the only nontrivial solutions are 2^3 (“two cubed”) and 3^2 (“three squared”). That conjecture by this man involves the (15[1])Diophantine equation [read slowly]: “x to the a minus y to the b equals one.” Euler used constructs named for this mathematician to calculate the number of ways to (*) triangulate a convex n+2-gon. This man’s namesake number is proportional to 2n choose n, thus one can derive his namesake numbers by taking the central column of Pascal’s triangle. For (-5[1])10 points, name this mathematician whose namesake numbers begin with 1, 1, 2, 5, and (10[1]0[1])14. ■END■