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Omni-MATH / Let …f:N→{0,1,…,16} such that f(x+17)=f(x) quad text { and } quad fleft(x^{2}right) equiv f(x)^{2}+15 quad(bmod 17) for all integers x≥1

Problem

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problem

Let \mathbb{N} denote the natural numbers. Compute the number of functions f:N→{0,1,…,16}f: \mathbb{N} \rightarrow\{0,1, \ldots, 16\} such that $$f(x+17)=f(x) \quad \text { and } \quad f\left(x^{2}\right) \equiv f(x)^{2}+15 \quad(\bmod 17)$$ for all integers x≥1x \geq 1
Plain-text mathematical notation (without MathML)
Let \mathbb{N} denote the natural numbers. Compute the number of functions f:N→{0,1,…,16} such that $$f(x+17)=f(x) \quad \text { and } \quad f\left(x^{2}\right) \equiv f(x)^{2}+15 \quad(\bmod 17)$$ for all integers x≥1
Original LaTeX notation
Let \mathbb{N} denote the natural numbers. Compute the number of functions $f: \mathbb{N} \rightarrow\{0,1, \ldots, 16\}$ such that $$f(x+17)=f(x) \quad \text { and } \quad f\left(x^{2}\right) \equiv f(x)^{2}+15 \quad(\bmod 17)$$ for all integers $x \geq 1$

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Source and history

task_id
09916486-76e6-5c33-8b33-688830622fa8
task_key
test--09916486-76e6-5c33-8b33-688830622fa8
task_revision_id
1
config / split
/ test

Official source

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