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IV Lusophon Mathematical Olympiad 2014 - Problem 5
IV Lusophon Mathematical Olympiad 2014 - Problem 5
Source:
December 28, 2014
number theory
divisibility tests
Problem Statement
Find all quadruples of positive integers
(
k
,
a
,
b
,
c
)
(k,a,b,c)
(
k
,
a
,
b
,
c
)
such that
2
k
=
a
!
+
b
!
+
c
!
2^k=a!+b!+c!
2
k
=
a
!
+
b
!
+
c
!
and
a
≥
b
≥
c
a\geq b\geq c
a
≥
b
≥
c
.
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