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Polynomials/Formula for X^odd+1/Exercise
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Prove the formula
X
u
+
1
=
(
X
+
1
)
(
X
u
−
1
−
X
u
−
2
+
X
u
−
3
−
⋯
+
X
2
−
X
+
1
)
{\displaystyle {}X^{u}+1=(X+1){\left(X^{u-1}-X^{u-2}+X^{u-3}-\cdots +X^{2}-X+1\right)}\,}
for
u
{\displaystyle {}u}
odd.
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