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2021 CMIMC
1.5
2021 Alg/NT Div 1 P5
2021 Alg/NT Div 1 P5
Source:
March 2, 2021
algebra
Problem Statement
Suppose
f
f
f
is a degree 42 polynomial such that for all integers
0
≤
i
≤
42
0\le i\le 42
0
≤
i
≤
42
,
f
(
i
)
+
f
(
43
+
i
)
+
f
(
2
⋅
43
+
i
)
+
⋯
+
f
(
46
⋅
43
+
i
)
=
(
−
2
)
i
f(i)+f(43+i)+f(2\cdot43+i)+\cdots+f(46\cdot43+i)=(-2)^i
f
(
i
)
+
f
(
43
+
i
)
+
f
(
2
⋅
43
+
i
)
+
⋯
+
f
(
46
⋅
43
+
i
)
=
(
−
2
)
i
Find
f
(
2021
)
−
f
(
0
)
f(2021)-f(0)
f
(
2021
)
−
f
(
0
)
.Proposed by Adam Bertelli
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