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2020-IMOC
N2
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Problems
(1)
nice diophantine with existence
Source: IMOC 2020 N2
8/13/2021
Find all positive integers
N
N
N
such that the following holds: There exist pairwise coprime positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
with
1
a
+
1
b
+
1
c
=
N
a
+
b
+
c
.
\frac1a+\frac1b+\frac1c=\frac N{a+b+c}.
a
1
+
b
1
+
c
1
=
a
+
b
+
c
N
.
Diophantine equation
number theory