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Czech-Polish-Slovak Match
2021 Czech-Austrian-Polish-Slovak Match
1
Routine number theory
Routine number theory
Source: 2021 Czech-Polish-Slovak Match, P1
August 3, 2021
Problem Statement
Find all quadruples
(
a
,
b
,
c
,
d
)
(a, b, c, d)
(
a
,
b
,
c
,
d
)
of positive integers satisfying
gcd
(
a
,
b
,
c
,
d
)
=
1
\gcd(a, b, c, d) = 1
g
cd
(
a
,
b
,
c
,
d
)
=
1
and
a
∣
b
+
c
,
b
∣
c
+
d
,
c
∣
d
+
a
,
d
∣
a
+
b
.
a | b + c, ~ b | c + d, ~ c | d + a, ~ d | a + b.
a
∣
b
+
c
,
b
∣
c
+
d
,
c
∣
d
+
a
,
d
∣
a
+
b
.
Vítězslav Kala (Czech Republic)
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