document.write( "Question 1158267: Find the last digit of the sum : 3^2018 + 4^2018 = ? \n" ); document.write( "

Algebra.Com's Answer #781172 by ikleyn(52799) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "n                    :     1    2    3    4    5    6    7    8    9    10      \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Last digit of   :        3    9    7    1    3    9    7    1    3     9\r\n" );
document.write( "\r\n" );
document.write( "Last digit of   :        4    6    4    6    4    6    4    6    4     6\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The last digits of the number    form a periodical sequence.\r\n" );
document.write( "\r\n" );
document.write( "The period starts from n= 1 and has the length of 4.\r\n" );
document.write( "\r\n" );
document.write( "2018 = 504*4 + 2.\r\n" );
document.write( "\r\n" );
document.write( "So the number   has the last digit 9:  the second digit in the cycle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The last digits of the number    form a periodical sequence.\r\n" );
document.write( "\r\n" );
document.write( "The period starts from n= 1 and has the length of 2.\r\n" );
document.write( "\r\n" );
document.write( "2018 = 1008*2 + 2.\r\n" );
document.write( "\r\n" );
document.write( "So the number   has the last digit 6:  the second digit in the cycle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the sum   +  has the last digit  9 + 6 = 5 (mod 10).     ANSWER\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( " \n" ); document.write( "

\n" );