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Omni-MATH / Define a power cycle to be a set S consisting of the nonnegative integer powers of an integer a, i.e. S={1,a,a²,…} for some integer a. What is the minimum number of power cycles re…

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problem

Define a power cycle to be a set SS consisting of the nonnegative integer powers of an integer aa, i.e. S={1,a,a2,…}S=\left\{1, a, a^{2}, \ldots\right\} for some integer aa. What is the minimum number of power cycles required such that given any odd integer nn, there exists some integer kk in one of the power cycles such that n≡kn \equiv k $(\bmod 1024) ?$
Plain-text mathematical notation (without MathML)
Define a power cycle to be a set S consisting of the nonnegative integer powers of an integer a, i.e. S={1,a,a²,…} for some integer a. What is the minimum number of power cycles required such that given any odd integer n, there exists some integer k in one of the power cycles such that n≡k $(\bmod 1024) ?$
Original LaTeX notation
Define a power cycle to be a set $S$ consisting of the nonnegative integer powers of an integer $a$, i.e. $S=\left\{1, a, a^{2}, \ldots\right\}$ for some integer $a$. What is the minimum number of power cycles required such that given any odd integer $n$, there exists some integer $k$ in one of the power cycles such that $n \equiv k$ $(\bmod 1024) ?$

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Source and history

task_id
88f9f270-6a5c-54ca-b111-bc56ccbd978a
task_key
test--88f9f270-6a5c-54ca-b111-bc56ccbd978a
task_revision_id
1
config / split
/ test

Official source

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