MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1967 Swedish Mathematical Competition
3
3
Part of
1967 Swedish Mathematical Competition
Problems
(1)
finitely many triples of positive (a, b, c) such that 1/a + 1/b + 1/c = 1/1000
Source: 1967 Swedish Mathematical Competition p3
3/21/2021
Show that there are only finitely many triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of positive integers such that
1
a
+
1
b
+
1
c
=
1
1000
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{1000}
a
1
+
b
1
+
c
1
=
1000
1
.
Diophantine equation
diophantine
number theory