document.write( "Question 1197923: What remainder is left when the number $\"%28567288133%29%5E6\"$ is divided by 8? \n" ); document.write( "

Algebra.Com's Answer #831389 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "It is easy to check directly that  567288133  gives the remainder  5  when divided by  8.\r\n" );
document.write( "\r\n" );
document.write( "By the way, for it, only three last digits of a number are important.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    We write  567288133 == 5 mod 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that   gives the remainder   when divided by 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Next,   = 15625.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is also easy to check directly that the remainder  {15625 mod 8}  is the same as  {1 mod 8}.\r\n" );
document.write( "\r\n" );
document.write( "    (and again, for it, only three last digits of the number 15625 do matter).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  When the number  is divided by 8, the remainder is 1.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "///////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "May the god save you from solving this problem in the way as @MathLover1 does it . . . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );