document.write( "Question 6689: Solve the equation:\r
\n" ); document.write( "\n" ); document.write( "233x + 177 = 496 (mod 792) \n" ); document.write( "
Algebra.Com's Answer #3674 by khwang(438)\"\" \"About 
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Solve
\n" ); document.write( " 233 x = 219 (mod 792)
\n" ); document.write( " Since 792 and 233 are relative prime(in fact 233 is prime)
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\n" ); document.write( " USe Euclidan algorithm to find the inverse of 233 in mod 792
\n" ); document.write( " 792 = 233 * 3 + 93,
\n" ); document.write( " 233 = 93*2 + 47,
\n" ); document.write( " 93 = 47*2 - 1
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\n" ); document.write( " Hence, -1 = 93 - 47*2
\n" ); document.write( " = 93 - (233 -93*2)*2
\n" ); document.write( " = 233*(-2) + 93*5
\n" ); document.write( " = 233*(-2) + (792 -233*3)*5
\n" ); document.write( " = 233*(-17) + 792*5\r
\n" ); document.write( "\n" ); document.write( " Or 233*17 + 792*(-5) = 1\r
\n" ); document.write( "\n" ); document.write( " Apply mod 792 on both sides, we have 233*17 = 1 mod 792.
\n" ); document.write( " This means 17 is the inverse of 233 mod 792.
\n" ); document.write( " Multiply 17 on both sides of 233 x = 219 (mod 792) , we get
\n" ); document.write( " x = 17* 219 mod 792 = 555 mod 792.\r
\n" ); document.write( "\n" ); document.write( " Use Excel, check MOD(233*555,792) = 219 OK
\n" ); document.write( " The answer x = 555 mod 792.
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\n" ); document.write( " Kenny\r
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