MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
22
22
Part of
PEN H Problems
Problems
(1)
H 22
Source:
5/25/2007
Find all integers
a
,
b
,
c
,
x
,
y
,
z
a,b,c,x,y,z
a
,
b
,
c
,
x
,
y
,
z
such that
a
+
b
+
c
=
x
y
z
,
x
+
y
+
z
=
a
b
c
,
a
≥
b
≥
c
≥
1
,
x
≥
y
≥
z
≥
1.
a+b+c=xyz, \; x+y+z=abc, \; a \ge b \ge c \ge 1, \; x \ge y \ge z \ge 1.
a
+
b
+
c
=
x
yz
,
x
+
y
+
z
=
ab
c
,
a
≥
b
≥
c
≥
1
,
x
≥
y
≥
z
≥
1.
symmetry
Diophantine Equations