63rd Annual STS (2003-2004)
Finalists
Silas Isaac Richelson

NEW YORK
Silas Isaac Richelson, 18, of Armonk, studied the primal Catalan's conjecture for his mathematics project in the Intel Science Talent Search. Silas's paper generalizes the well-known Catalan's Conjecture to quadratic fields -- fields obtained by adding a square root to some nonsquare integer. Catalan's Conjecture says that 8 (which is 23) and 9 (which is 32) are the only solutions to 1 + xn = ym where x, y, n, m are all integers greater than 1. The classical Catalan's Conjecture, posed in 1844, is a seemingly simple statement about numbers which has only recently been proved by Preda Mihailescu. Silas shows there are no other integer solutions with both x and y prime, and he gives analogous results for quadratic fields. At Byram Hills High School, Silas received the Award for Excellence in Mathematics, is the first tenor saxophone in the band and enjoys varsity soccer and baseball, math club, camping and peer tutoring. He also performed 200 hours of volunteer work at a nearby hospital last summer. The son of Eric and Sara Richelson, Silas plans to study applied math or physics at Stanford and one day work in industry, where he hopes to "face real problems and discover creative solutions."