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All-Russian Olympiad
1980 All Soviet Union Mathematical Olympiad
297
297
Part of
1980 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 297 All Soviet Union MO 1980 n_{k+1} = n_k + P(n_k), product of digits
Source:
7/19/2019
Let us denote with
P
(
n
)
P(n)
P
(
n
)
the product of all the digits of
n
n
n
. Consider the sequence
n
k
+
1
=
n
k
+
P
(
n
k
)
n_{k+1} = n_k + P(n_k)
n
k
+
1
=
n
k
+
P
(
n
k
)
Can it be unbounded for some
n
1
n_1
n
1
?
product of digits
number theory
Sequence