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Find the number of functions $f(n),$ taking the integers to the integers, such that \[f(a + b) + f(ab) = f(a) f(b) + 1\]for all integers $a$ and $b.$

 Sep 29, 2020
 #1
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There are 5 functions that work.

 Sep 30, 2020
 #2
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That is incorrect. :(

Guest Sep 30, 2020

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