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Putnam
1988 Putnam
B1
B1
Part of
1988 Putnam
Problems
(1)
Putnam 1988 B1
Source:
8/6/2019
A composite (positive integer) is a product
a
b
ab
ab
with
a
a
a
and
b
b
b
not necessarily distinct integers in
{
2
,
3
,
4
,
…
}
\{2,3,4,\dots\}
{
2
,
3
,
4
,
…
}
. Show that every composite is expressible as
x
y
+
x
z
+
y
z
+
1
xy+xz+yz+1
x
y
+
x
z
+
yz
+
1
, with
x
,
y
,
z
x,y,z
x
,
y
,
z
positive integers.
Putnam