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National and Regional Contests
PEN Problems
PEN H Problems
79
79
Part of
PEN H Problems
Problems
(1)
H 79
Source:
5/25/2007
Find all positive integers
m
m
m
and
n
n
n
for which
1
!
+
2
!
+
3
!
+
⋯
+
n
!
=
m
2
1!+2!+3!+\cdots+n!=m^{2}
1
!
+
2
!
+
3
!
+
⋯
+
n
!
=
m
2
modular arithmetic
Diophantine Equations