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Omni-MATH / Consider all functions f:Z→Z satisfying f(f(x)+2x+20)=15 Call an integer n good if f(n) can take any integer value. In other words, if we fix n, for any integer m, there exists a f…

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problem

Consider all functions f:Z→Zf: \mathbb{Z} \rightarrow \mathbb{Z} satisfying f(f(x)+2x+20)=15f(f(x)+2 x+20)=15 Call an integer nn good if f(n)f(n) can take any integer value. In other words, if we fix nn, for any integer mm, there exists a function ff such that f(n)=mf(n)=m. Find the sum of all good integers xx.
Plain-text mathematical notation (without MathML)
Consider all functions f:Z→Z satisfying f(f(x)+2x+20)=15 Call an integer n good if f(n) can take any integer value. In other words, if we fix n, for any integer m, there exists a function f such that f(n)=m. Find the sum of all good integers x.
Original LaTeX notation
Consider all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ satisfying $$f(f(x)+2 x+20)=15$$ Call an integer $n$ good if $f(n)$ can take any integer value. In other words, if we fix $n$, for any integer $m$, there exists a function $f$ such that $f(n)=m$. Find the sum of all good integers $x$.

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Source and history

task_id
16ec7907-f71d-5053-9c36-f9e7b6867695
task_key
test--16ec7907-f71d-5053-9c36-f9e7b6867695
task_revision_id
1
config / split
/ test

Official source

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