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2020 LMT Spring
20
20
Part of
2020 LMT Spring
Problems
(1)
Spring 2020 Team Round Problem 20
Source:
8/22/2020
Let
c
1
<
c
2
<
c
3
c_1<c_2<c_3
c
1
<
c
2
<
c
3
be the three smallest positive integer values of
c
c
c
such that the distance between the parabola
y
=
x
2
+
2020
y=x^2+2020
y
=
x
2
+
2020
and the line
y
=
c
x
y=cx
y
=
c
x
is a rational multiple of
2
\sqrt{2}
2
. Compute
c
1
+
c
2
+
c
3
c_1+c_2+c_3
c
1
+
c
2
+
c
3
.