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International Contests
Tournament Of Towns
1993 Tournament Of Towns
(387) 5
(387) 5
Part of
1993 Tournament Of Towns
Problems
(1)
TOT 387 1993 Autumn A J5 n +S(n) = p + S(p) = q + S(q), sum of digits
Source:
6/12/2024
Let
S
(
n
)
S(n)
S
(
n
)
denote the sum of digits of
n
n
n
(in decimal representation). Do there exist three different natural numbers
n
n
n
,
p
p
p
and
q
q
q
such that
n
+
S
(
n
)
=
p
+
S
(
p
)
=
q
+
S
(
q
)
?
n +S(n) = p + S(p) = q + S(q)?
n
+
S
(
n
)
=
p
+
S
(
p
)
=
q
+
S
(
q
)?
(M Gerver)
number theory
sum of digits