Solutions to p^2 Divides 10^p - 10

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Theorem

The known prime numbers $p$ which satisfy the equation:

$p^2 \divides \paren {10^p - 10}$

where $\divides$ denotes divisibility, are:

$3, 487, 56 \, 598 \, 313$

This sequence is A045616 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof


Also see


Sources