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Tournament Of Towns
1991 Tournament Of Towns
(307) 4
(307) 4
Part of
1991 Tournament Of Towns
Problems
(1)
TOT 307 1991 Autumn A J4 a_{k+1}=3a_k^4+4a_k^3, NT
Source:
6/9/2024
A sequence
a
n
a_n
a
n
is determined by the rules
a
0
=
9
a_0 = 9
a
0
=
9
and for any nonnegative
k
k
k
,
a
k
+
1
=
3
a
k
4
+
4
a
k
3
.
a_{k+1}=3a_k^4+4a_k^3.
a
k
+
1
=
3
a
k
4
+
4
a
k
3
.
Prove that
a
10
a_{10}
a
10
contains more than
1000
1000
1000
nines in decimal notation.(Yao)
number theory
Digits
recurrence relation