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Putnam
1947 Putnam
B5
B5
Part of
1947 Putnam
Problems
(1)
Putnam 1947 B5
Source: Putnam 1947
4/3/2022
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be distinct integers such that
(
x
−
a
)
(
x
−
b
)
(
x
−
c
)
(
x
−
d
)
−
4
=
0
(x-a)(x-b)(x-c)(x-d) -4=0
(
x
−
a
)
(
x
−
b
)
(
x
−
c
)
(
x
−
d
)
−
4
=
0
has an integer root
r
.
r.
r
.
Show that
4
r
=
a
+
b
+
c
+
d
.
4r=a+b+c+d.
4
r
=
a
+
b
+
c
+
d
.
Putnam
Integer Polynomial
roots