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Baltic Way
2023 Baltic Way
17
17
Part of
2023 Baltic Way
Problems
(1)
Sum of digits NT part 1
Source: Baltic Way 2023/17
11/11/2023
Find all pairs of positive integers
(
a
,
b
)
(a, b)
(
a
,
b
)
, such that
S
(
a
b
+
1
)
=
a
b
S(a^{b+1})=a^b
S
(
a
b
+
1
)
=
a
b
, where
S
(
m
)
S(m)
S
(
m
)
denotes the digit sum of
m
m
m
.
number theory