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Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2017 Latvia Baltic Way TST
14
14
Part of
2017 Latvia Baltic Way TST
Problems
(1)
ab + bc + ac = (a + b -c)(b + c - a)(c + a - b) for gcd(a,b,c)=1
Source: 2017 Latvia BW TST P14
12/18/2022
Can you find three natural numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
whose greatest common divisor is
1
1
1
and which satisfy the equality
a
b
+
b
c
+
a
c
=
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
?
ab + bc + ac = (a + b -c)(b + c - a)(c + a - b) ?
ab
+
b
c
+
a
c
=
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)?
number theory
Diophantine Equations
diophantine