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$f\colon\Bbb Z\to\{28,29\}~,~ f(x)= \begin{cases} 29 \ \ \text{if} \ [x] \in \{[4k]\mid 0\leq k\leq 99~\land~k\notin\{25,50,75\}\} \ \\ 28 \ \text{otherwise} \end{cases}$

Find a function $g\colon\Bbb Z^+\cup\{0\}\to\{28,29\}$ which is not piece-wise defined and is identical to $f$ in its own domain.

The function you should be seeking for might not be that mathematical....

Clarifications:

$[x]$ denotes the congruence class of $x$ modulo $400$ .

This problem is original

#NumberTheory

Easy Math Editor

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Comments

I do not understand the problem. We already have defined f in the problem statement. How can we improve upon that?

Agnishom Chattopadhyay - 5 years, 4 months ago

You have to find all f(x) which have those two properties.