document.write( "Question 1143912: Please show solving for 5x = 1(mod8) \n" ); document.write( "

Algebra.Com's Answer #764883 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Since the multiplier  \" 5 \" and the module \"8\" are mutually prime numbers,\r\n" );
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document.write( "the general theory says that this modular equation has the solution, and the solution is unique as the number module 8.\r\n" );
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document.write( "The method to find the solution is  \"trial and error\".\r\n" );
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document.write( "Do not afraid and do not be scared. To find the solution, you need to check only 8 numbers module 8.\r\n" );
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document.write( "These numbers to check are 0 mod8, 1 mod8, 2 mod8, 3 mod8, 4 mod8, 5 mod8, 6 mod8 and 7 mod8.\r\n" );
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document.write( "The solutions INEVITABLY  is among these numbers.\r\n" );
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document.write( "Doing in this way, you will quickly find that x= 5 mod8 is the solution.\r\n" );
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document.write( "Indeed, 5*5 = 25 = 1 mod8.\r\n" );
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document.write( "It means that the solutions are all integer numbers that give the remainder 5 when are divided by 8.\r\n" );
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document.write( "In other words, all integer numbers of the form  n = 5 + 8k,  k = 0, +/-1, +/-2, . . . \r\n" );
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\n" ); document.write( "\n" ); document.write( "Answered, explained and completed.\r
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