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Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
1993 Mexico National Olympiad
4
4
Part of
1993 Mexico National Olympiad
Problems
(1)
f(n,k): f(n,0)=f(n,n)=1 and f(n,k)=f(n-1,k-1)+f(n-1,k) for 0<k<n , f(3991,1993)
Source: Mexican Mathematical Olympiad 1993 OMM P4
7/29/2018
f
(
n
,
k
)
f(n,k)
f
(
n
,
k
)
is defined by (1)
f
(
n
,
0
)
=
f
(
n
,
n
)
=
1
f(n,0) = f(n,n) = 1
f
(
n
,
0
)
=
f
(
n
,
n
)
=
1
and (2)
f
(
n
,
k
)
=
f
(
n
−
1
,
k
−
1
)
+
f
(
n
−
1
,
k
)
f(n,k) = f(n-1,k-1) + f(n-1,k)
f
(
n
,
k
)
=
f
(
n
−
1
,
k
−
1
)
+
f
(
n
−
1
,
k
)
for
0
<
k
<
n
0 < k < n
0
<
k
<
n
. How many times do we need to use (2) to find
f
(
3991
,
1993
)
f(3991,1993)
f
(
3991
,
1993
)
?
number theory
function
recursive