Question

Prove: Use R - 3L for divisibility by 31.

Answer 1

$N=10R+L\\R-3L=-3\left( 10R+L \right) +31R\\Thus\,\,31|R-3L\Leftrightarrow 31|3\left( 10R+L \right) \Leftrightarrow 31|10R+L=N\\\left( we\,\,use\,\,the\,\,fact\,\,that\,\,3and\,\,31are\,\,mutually\,\,prime \right)$