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Netherlands Contests
Dutch Mathematical Olympiad
1997 Dutch Mathematical Olympiad
1
1
Part of
1997 Dutch Mathematical Olympiad
Problems
(1)
f(n) is product of sum of digits of n with n itself , f (n) = 19091997
Source: Dutch NMO 1997 p1
1/29/2020
For each positive integer
n
n
n
we define
f
(
n
)
f (n)
f
(
n
)
as the product of the sum of the digits of
n
n
n
with
n
n
n
itself. Examples:
f
(
19
)
=
(
1
+
9
)
×
19
=
190
f (19) = (1 + 9) \times 19 = 190
f
(
19
)
=
(
1
+
9
)
×
19
=
190
,
f
(
97
)
=
(
9
+
7
)
×
97
=
1552
f (97) = (9 + 7) \times 97 = 1552
f
(
97
)
=
(
9
+
7
)
×
97
=
1552
. Show that there is no number
n
n
n
with
f
(
n
)
=
19091997
f (n) = 19091997
f
(
n
)
=
19091997
.
number theory
sum of digits
Product