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Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
56
56
Part of
PEN H Problems
Problems
(1)
H 56
Source:
5/25/2007
Prove that the equation
∏
c
y
c
(
x
1
−
x
2
)
=
∏
c
y
c
(
x
1
−
x
3
)
\prod_{cyc} (x_1-x_2)= \prod_{cyc} (x_1-x_3)
∏
cyc
(
x
1
−
x
2
)
=
∏
cyc
(
x
1
−
x
3
)
has a solution in natural numbers where all
x
i
x_i
x
i
are different.
Diophantine Equations