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Purple Comet Problems
2003 Purple Comet Problems
23
Problem 23, Fall 2003 , MS and HS
Problem 23, Fall 2003 , MS and HS
Source:
June 23, 2011
function
Problem Statement
For each positive integer
m
m
m
and
n
n
n
define function
f
(
m
,
n
)
f(m, n)
f
(
m
,
n
)
by
f
(
1
,
1
)
=
1
f(1, 1) = 1
f
(
1
,
1
)
=
1
,
f
(
m
+
1
,
n
)
=
f
(
m
,
n
)
+
m
f(m+ 1, n) = f(m, n) +m
f
(
m
+
1
,
n
)
=
f
(
m
,
n
)
+
m
and
f
(
m
,
n
+
1
)
=
f
(
m
,
n
)
ā
n
f(m, n + 1) = f(m, n) - n
f
(
m
,
n
+
1
)
=
f
(
m
,
n
)
ā
n
. Find the sum of all the values of
p
p
p
such that
f
(
p
,
q
)
=
2004
f(p, q) = 2004
f
(
p
,
q
)
=
2004
for some
q
q
q
.
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