New answers tagged golden-ratio
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Finding functions $h$ satisfying $h(h(n))+h(n+1) = n+2$ for all natural $n$. Why does the Golden Ratio appear?
Suppose that $h(n) = an + b$. Then the equation becomes:
$$a(an + b) + b + a(n + 1) = n + 2$$
$$a^2n + ab + b + an + a = n + 2$$
$$(a^2 + a - 1)n + ab + a + b - 2 = 0$$
For this to be satisfied for ...
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