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Ecuador Mathematical Olympiad (OMEC)
2020 Ecuador NMO (OMEC)
2
2
Part of
2020 Ecuador NMO (OMEC)
Problems
(1)
Equation with rational integers and no integers numbers
Source: OMEC Ecuador National Olympiad Final Round 2020 N3 P2 day 1
11/10/2024
Find all pairs
(
n
,
q
)
(n, q)
(
n
,
q
)
such that
n
n
n
is a positive integer,
q
q
q
is a not integer rational and
n
q
ā
q
n^q-q
n
q
ā
q
is an integer.
number theory
national olympiad