document.write( "Question 1207685: The inverse of $a$ modulo $44$ is $b$. What is the inverse of $9$ modulo $10$? \n" ); document.write( "

Algebra.Com's Answer #845695 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The inverse of a modulo 44 is b. What is the inverse of 9 modulo 10?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Inverse of 9 modulo 10 is an integer number  1 <= n <= 9  such that the product\r\n" );
document.write( "\r\n" );
document.write( "    n*9 is equal to 1 modulo 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "As soon as you pronounce these words mentally (as the definition), the answer just should be in your mind:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +-----------------------------------------------------------+\r\n" );
document.write( "    |    the inverse of 9 modulo 10 is the number 9 modulo 10.  |\r\n" );
document.write( "    +-----------------------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Indeed, 9*9 = 81, which is equal to 1 modulo 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The inverse of 9 modulo 10 is the number 9 modulo 10.\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( "This problem consists of two statements.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Of these two statements, the first one does not bring any relevant information;
\n" ); document.write( "therefore, having sanity in the skull, we should ignore this first statement
\n" ); document.write( "(by pointing that it is non-sensical).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The second statement brings the question and makes sense (even if consider it
\n" ); document.write( "independently of the first statement).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So, I ignore first statement (as if it is empty and as if it does not exist)
\n" ); document.write( "and react to the second statement - it is precisely what I do.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        ************************************************\r
\n" ); document.write( "\n" ); document.write( "            In this problem formulation, the first statement\r
\n" ); document.write( "\n" ); document.write( "            does not carry any information, is not necessary \r
\n" ); document.write( "\n" ); document.write( "            and interferes with understanding the rest of the task.\r
\n" ); document.write( "\n" ); document.write( "        ************************************************\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );