document.write( "Question 1020241: Prove that 3 divides 20^2n − 1 for all n = 0, 1, 2, 3, . . .. \n" ); document.write( "

Algebra.Com's Answer #636146 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"20%5E%282n%29-1=400%5En-1\"$
\n" ); document.write( "When $\"n=0\"$ ,
\n" ); document.write( " $\"400%5E%28m%29-1=1-1=0\"$ divisible by 3.
\n" ); document.write( "When $\"n=1\"$ ,
\n" ); document.write( " $\"400%5E%28n%29-1=400-1=399\"$ divisible by 3 since it ends in 9.
\n" ); document.write( "When $\"n=2\"$ ,
\n" ); document.write( " $\"400%5E%28n%29-1=160000-1=159999\"$ divisible by 3 since it ends in 9.
\n" ); document.write( "As you see the number is a power of 400 so the last digit will always be 0.
\n" ); document.write( "Subtracting 1 makes it the last digit a 9 so it will always be divisible by 3. \n" ); document.write( "

\n" );