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Omni-MATH / Let N be the smallest positive integer for which x²+x+1 divides 166−∑_(d∣N,d>0)x^(d) Find the remainder when N is divided by 1000.

Problem

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problem

Let NN be the smallest positive integer for which x2+x+1 divides 166−∑d∣N,d>0xdx^{2}+x+1 \quad \text { divides } \quad 166-\sum_{d \mid N, d>0} x^{d} Find the remainder when NN is divided by 1000.
Plain-text mathematical notation (without MathML)
Let N be the smallest positive integer for which x²+x+1  divides  166−∑_(d∣N,d>0)x^(d) Find the remainder when N is divided by 1000.
Original LaTeX notation
Let $N$ be the smallest positive integer for which $$x^{2}+x+1 \quad \text { divides } \quad 166-\sum_{d \mid N, d>0} x^{d}$$ Find the remainder when $N$ is divided by 1000.

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Source and history

task_id
a44996a0-f8e4-5a4d-a387-f3e48fbeb60e
task_key
test--a44996a0-f8e4-5a4d-a387-f3e48fbeb60e
task_revision_id
1
config / split
/ test

Official source

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