Answer to Question #326608 in Combinatorics | Number Theory for Allen

Question

Prove: Methods for divisibility by 13.

1. Method 2. ( R + 4L) 

Answer 1

$N=10L+R\\N=10L+R=10\left( L+4R \right) -39R\\Hence\,\,13|N\,\,iff\,\,13|10\left( L+4R \right) \\Since\,\,10 and\,\,13 are\,\,mutually\,\,prime, we\,\,have\\13|L+4R$