Unformatted text preview: is divisible by , with B–5 Given a ﬁnite string of symbols
and , we write
for the number of ’s in minus the number
of ’s. For example,
. We
call a string balanced if every substring of (consecutive symbols of) has
. Thus,
is not balanced, since it contains the substring
. Find, with proof, the number of balanced strings of length .
)# !
$0( '
# !
$¥( '&% [email protected]"&&
# !
6 A–5 If is a prime number greater than 3 and
prove that the sum to
. matrix Q
!s } E...
View
Full Document
 Fall '08
 Staff
 Math, Real Numbers, Natural number, William Lowell Putnam Mathematical Competition

Click to edit the document details