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Ecuador Mathematical Olympiad (OMEC)
2021 Ecuador NMO (OMEC)
6
6
Part of
2021 Ecuador NMO (OMEC)
Problems
(1)
Diophantine equation with HIGH values
Source: OMEC Ecuador National Olympiad Final Round 2021 N3 P6 day 2
11/8/2024
Find all positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
such that
a
b
+
1
ab+1
ab
+
1
and
c
c
c
are coprimes and:
a
(
b
a
+
1
)
(
c
a
2
+
b
a
+
1
)
=
202
1
2021
a(ba+1)(ca^2+ba+1)=2021^{2021}
a
(
ba
+
1
)
(
c
a
2
+
ba
+
1
)
=
202
1
2021
number theory
Diophantine equation