Matt Miller
Northern Arizona University
Number Theoretic Properties of Pascal's Triangle.
Abstract:
Consider six binomial coefficients, situated in Pascal's Triangle so that they
are the corners of a small, regular hexagon with two numbers per side.
Divide
them into two sets by taking alternating entries. Each set's points now
are
the corners of an equilateral triangle, and joining the lines between them
forms a Star of David. The greatest common divisors of these two sets are
equal, a theorem posed by Hoggatt and proven by Gould
in 1971, and which he
referred to as "The Star of David Property."
Work has been done to generalize this result to hexagons with three and four
entries per side by Long and Sato, and some unpublished work has been done
regarding hexagons with 6 points per side. This presentation concerns
hexagons with an odd prime number of points per side, of arbitrary size but of
form 4k+1, and an unusual GCD property of such hexagons when particularly
situated.
(End of abstract)
I'll be presenting in Powerpoint. I'd like a
twenty minute slot, mid-late
morning on Saturday if possible.
Thanks,
Matt Miller
Northern
(928)226-7011