MathDB
Problems
Contests
Undergraduate contests
Putnam
2020 Putnam
B5
B5
Part of
2020 Putnam
Problems
(1)
Putnam 2020 B5
Source: 81st William Lowell Putnam Competition
2/22/2021
For
j
∈
{
1
,
2
,
3
,
4
}
j \in \{ 1,2,3,4\}
j
∈
{
1
,
2
,
3
,
4
}
, let
z
j
z_j
z
j
be a complex number with
∣
z
j
∣
=
1
| z_j | = 1
∣
z
j
∣
=
1
and
z
j
≠
1
z_j \neq 1
z
j
=
1
. Prove that
3
−
z
1
−
z
2
−
z
3
−
z
4
+
z
1
z
2
z
3
z
4
≠
0.
3 - z_1 - z_2 - z_3 - z_4 + z_1z_2z_3z_4 \neq 0.
3
−
z
1
−
z
2
−
z
3
−
z
4
+
z
1
z
2
z
3
z
4
=
0.
Putnam
Putnam 2020