document.write( "Question 1197910: Find the last two digits in the decimal numeral for (3¹⁶⁷)⁹⁵ \r
\n" ); document.write( "\n" ); document.write( "A) 27
\n" ); document.write( "B) 43
\n" ); document.write( "C) 81
\n" ); document.write( "D) 29
\n" ); document.write( "E) 07
\n" ); document.write( "

Algebra.Com's Answer #831369 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Last two digits ≡ Remainder when divided by \"100\"\r
\n" ); document.write( "\n" ); document.write( "φ\"%28100%29=4%2F5%2A1%2F2=40\"\r
\n" ); document.write( "\n" ); document.write( "By Euler’s theorem ,\"3%5E40\"\"1\" mod \"100\"\r
\n" ); document.write( "\n" ); document.write( "\"3%5E167=%283%5E40%29%5E4%2A3%5E7\"\"1%2A3%5E7\" mod \"100\"\r
\n" ); document.write( "\n" ); document.write( "≡\"3%2A3%5E6\"\r
\n" ); document.write( "\n" ); document.write( "≡\"3%2A%28700%2B29%29\"
\n" ); document.write( "≡\"87\" mod \"100\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%283%5E167%29%5E95\"\"87%5E95+\" mod \"100\"\r
\n" ); document.write( "\n" ); document.write( "≡\"%2887%5E40%29%5E2%2A87%5E15\"\r
\n" ); document.write( "\n" ); document.write( "≡\"87%5E15\" mod \"100\"......\"87=100-13\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "≡\"%28100++-++13%29%5E15\"\r
\n" ); document.write( "\n" ); document.write( "≡\"-13%5E15\"\r
\n" ); document.write( "\n" ); document.write( "≡\"-%2813%5E3%29%5E5\"\r
\n" ); document.write( "\n" ); document.write( "≡\"-%282200++-++3%29%5E5\"\r
\n" ); document.write( "\n" ); document.write( "≡\"3%5E5\"\r
\n" ); document.write( "\n" ); document.write( "≡\"3%2A%28100++-++19%29\"\"-57+\"\"43\" mod \"100\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "answer:\r
\n" ); document.write( "\n" ); document.write( "B)\"+43\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );