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Swedish Mathematical Competition
1998 Swedish Mathematical Competition
1
1
Part of
1998 Swedish Mathematical Competition
Problems
(1)
(8a-5b)^2 + (3b-2c)^2 + (3c-7a)^2 = 2
Source: 1998 Swedish Mathematical Competition p1
4/2/2021
Find all positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
, such that
(
8
a
−
5
b
)
2
+
(
3
b
−
2
c
)
2
+
(
3
c
−
7
a
)
2
=
2
(8a-5b)^2 + (3b-2c)^2 + (3c-7a)^2 = 2
(
8
a
−
5
b
)
2
+
(
3
b
−
2
c
)
2
+
(
3
c
−
7
a
)
2
=
2
.
number theory
diophantine
Diophantine equation