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National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2006 Bosnia and Herzegovina Junior BMO TST
1
1
Part of
2006 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
1/x + 2/y + 3/z = 1, diophantine, x > y > z
Source: 2006 Bosnia & Herzegovina JBMO TST p1
5/27/2020
. Find all triplets
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
,
x
>
y
>
z
x > y > z
x
>
y
>
z
of positive integers such that
1
x
+
2
y
+
3
z
=
1
\frac{1}{x}+\frac{2}{y}+\frac{3}{z}= 1
x
1
+
y
2
+
z
3
=
1
number theory
diophantine
Diophantine equation