66th Annual STS (2006-2007)
Finalists
Sohan Venkat Mikkilineni
MICHIGAN
Sohan Venkat Mikkilineni, 17, of Bloomfield Hills, submitted an Intel
Science Talent Search mathematics project that analyzed determinantal sequences.
A d-determinantal sequence is a doubly infinite sequence of integers
(..., an-1, an, an+1,...) such that the
two-by-two determinant anan+3 - an+1an+2 = d.
Note that three consecutive entries, together with d, determine the sequence. For
¦d¦>1 and where there is no common divisor of all the terms with odd indices
(and similarly for even indices), Sohan proved that there are, with few
exceptions, only finitely many solutions. By setting x = a1, y = a2 one sees a
link between determinantal sequences and those solutions of the equation
ax2 + abxy - by2 = -d with none of the pairs
(x,b), (y,a) and (x,y) having a
non-trivial common divisor. Sohan attends Detroit Country Day School in Beverly
Hills, and is captain of the F.I.R.S.T. Robotics Club. His scientific
achievements have earned him a certificate of tribute from Governor Granholm. An
accomplished cellist, Sohan is a member of the Detroit Civic Sinfonia Orchestra.
The son of Drs. Prasad and Jhansi Mikkilineni, he plans to study pre-medicine at
MIT or Stanford.
