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All-Russian Olympiad Regional Round
2024 All-Russian Olympiad Regional Round
10.9
Primes and divisibility
Primes and divisibility
Source: ARO Regional stage 2024 10.9
February 2, 2024
number theory
Problem Statement
Find all triplets
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of positive integers, such that
a
+
b
c
,
b
+
a
c
,
c
+
a
b
a+bc, b+ac, c+ab
a
+
b
c
,
b
+
a
c
,
c
+
ab
are primes and all divide
(
a
2
+
1
)
(
b
2
+
1
)
(
c
2
+
1
)
(a^2+1)(b^2+1)(c^2+1)
(
a
2
+
1
)
(
b
2
+
1
)
(
c
2
+
1
)
.
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