For today's date, 19-1-23, we have a beautiful representation of 19123 as a sum of the powers of \(\varphi\) (golden ratio).
\[19123=\displaystyle\sum_{k\in\mathcal{S}}\varphi^k=\sum_{k\in\mathcal{S}}\left(\dfrac{1+\sqrt{5}}{2}\right)^k\]

where the sum extends over all \(k\in\mathcal{S}=\{-20,-18,-15,-13,-10,-7,-4,-2,1,4,6,9,12,17,20\}\).

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