MathDB

Putnam 1987 B6

Source:

August 5, 2019

Putnam

Problem Statement

Let

F

be the field of

p^2

elements, where

p

is an odd prime. Suppose

S

is a set of

(p^2-1)/2

distinct nonzero elements of

F

with the property that for each

a\neq 0

in

F

, exactly one of

a

and

-a

is in

S

. Let

N

be the number of elements in the intersection

S \cap \{2a: a \in S\}

. Prove that

N

is even.

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