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2023 LMT Fall
20
2023 Fall LMT Speed p20 - x^{100} -x^{99} +... -x +1:(x^2 -1)
2023 Fall LMT Speed p20 - x^{100} -x^{99} +... -x +1:(x^2 -1)
Source:
March 2, 2024
algebra
Problem Statement
The remainder when
x
100
−
x
99
+
.
.
.
−
x
+
1
x^{100} -x^{99} +... -x +1
x
100
−
x
99
+
...
−
x
+
1
is divided by
x
2
−
1
x^2 -1
x
2
−
1
can be written in the form
a
x
+
b
ax +b
a
x
+
b
. Find
2
a
+
b
2a +b
2
a
+
b
.Proposed by Calvin Garces
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