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27
Smallest integer n for f(n)=5 given an identity
Smallest integer n for f(n)=5 given an identity
Source:
October 12, 2010
function
algebra unsolved
algebra
Problem Statement
The function
f
(
n
)
f(n)
f
(
n
)
is defined on the nonnegative integers
n
n
n
by:
f
(
0
)
=
0
,
f
(
1
)
=
1
f(0) = 0, f(1) = 1
f
(
0
)
=
0
,
f
(
1
)
=
1
, and
f
(
n
)
=
f
(
n
−
1
2
m
(
m
−
1
)
)
−
f
(
1
2
m
(
m
+
1
)
−
n
)
f(n) = f\left(n -\frac{1}{2}m(m - 1)\right)-f\left(\frac{1}{2}m(m+ 1)-n\right)
f
(
n
)
=
f
(
n
−
2
1
m
(
m
−
1
)
)
−
f
(
2
1
m
(
m
+
1
)
−
n
)
for
1
2
m
(
m
−
1
)
<
n
≤
1
2
m
(
m
+
1
)
,
m
≥
2
\frac{1}{2}m(m - 1) < n \le \frac{1}{2}m(m+ 1), m \ge 2
2
1
m
(
m
−
1
)
<
n
≤
2
1
m
(
m
+
1
)
,
m
≥
2
. Find the smallest integer
n
n
n
for which
f
(
n
)
=
5
f(n) = 5
f
(
n
)
=
5
.
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