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Caucasus Mathematical Olympiad
2022 Caucasus Mathematical Olympiad
5
5
Part of
2022 Caucasus Mathematical Olympiad
Problems
(1)
Diophantine equation in integers with odd digits
Source: VII Caucasus Mathematical Olympiad
3/13/2022
Let
S
S
S
be the set of all
5
6
5^6
5
6
positive integers, whose decimal representation consists of exactly 6 odd digits. Find the number of solutions
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of the equation
x
+
y
=
10
z
x+y=10z
x
+
y
=
10
z
, where
x
∈
S
x\in S
x
∈
S
,
y
∈
S
y\in S
y
∈
S
,
z
∈
S
z\in S
z
∈
S
.
combinatorics