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17S. A Hidden Divisibility

A13 Show that for all prime numbers $p$,

$Q(p) = \prod^{p - 1}_{k = 1}k^{2k - p - 1}$

is an integer.

Here is the official solution file: pen17.pdf.

17. A Hidden Divisibility

A13 Show that for all prime numbers $p$,

$Q(p) = \prod^{p - 1}_{k = 1}k^{2k - p - 1}$

is an integer.