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Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2019 Latvia Baltic Way TST
16
16
Part of
2019 Latvia Baltic Way TST
Problems
(1)
System of equations with factorials
Source: Latvian TST for Baltic Way 2019 Problem 16
5/29/2020
Determine all tuples of positive integers
(
x
,
y
,
z
,
t
)
(x, y, z, t)
(
x
,
y
,
z
,
t
)
such that:
x
y
z
=
t
!
xyz = t!
x
yz
=
t
!
(
x
+
1
)
(
y
+
1
)
(
z
+
1
)
=
(
t
+
1
)
!
(x+1)(y+1)(z+1) = (t+1)!
(
x
+
1
)
(
y
+
1
)
(
z
+
1
)
=
(
t
+
1
)!
holds simultaneously.
algebra
system of equations
factorial