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Putnam
2022 Putnam
A1
2022 Putnam A1
2022 Putnam A1
Source:
December 4, 2022
Putnam
Putnam 2022
Problem Statement
Determine all ordered pairs of real numbers
(
a
,
b
)
(a,b)
(
a
,
b
)
such that the line
y
=
a
x
+
b
y=ax+b
y
=
a
x
+
b
intersects the curve
y
=
ln
(
1
+
x
2
)
y=\ln(1+x^2)
y
=
ln
(
1
+
x
2
)
in exactly one point.
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