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National and Regional Contests
PEN Problems
PEN P Problems
26
26
Part of
PEN P Problems
Problems
(1)
P 26
Source:
5/25/2007
Let
a
,
b
a, b
a
,
b
and
c
c
c
be positive integers, no two of which have a common divisor greater than
1
1
1
. Show that
2
a
b
c
−
a
b
−
b
c
−
c
a
2abc-ab-bc-ca
2
ab
c
−
ab
−
b
c
−
c
a
is the largest integer which cannot be expressed in the form
x
b
c
+
y
c
a
+
z
a
b
xbc+yca+zab
x
b
c
+
yc
a
+
z
ab
, where
x
,
y
,
z
∈
N
0
x, y, z \in \mathbb{N}_{0}
x
,
y
,
z
∈
N
0
Additive Number Theory