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2020 ASDAN Math Tournament
8
8
Part of
2020 ASDAN Math Tournament
Problems
(1)
2020 Team #8
Source:
10/24/2023
For nonzero integers
n
n
n
, let
f
(
n
)
f(n)
f
(
n
)
be the sum of all positive integers
b
b
b
for which all solutions
x
x
x
to
x
2
+
b
x
+
n
=
0
x^2 +bx+n = 0
x
2
+
b
x
+
n
=
0
are integers, and let
g
(
n
)
g(n)
g
(
n
)
be the sum of all positive integers
c
c
c
for which all solutions
x
x
x
to
c
x
+
n
=
0
cx + n = 0
c
x
+
n
=
0
are integers. Compute
∑
n
=
1
2020
(
f
(
n
)
−
g
(
n
)
)
\sum^{2020}_{n=1} (f(n) - g(n))
∑
n
=
1
2020
(
f
(
n
)
−
g
(
n
))
.
team test