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Lusophon Mathematical Olympiad
2014 Lusophon Mathematical Olympiad
5
5
Part of
2014 Lusophon Mathematical Olympiad
Problems
(1)
IV Lusophon Mathematical Olympiad 2014 - Problem 5
Source:
12/28/2014
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
.
number theory
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