document.write( "Question 77052: Use the factor theorem to show that if 2^p - 1, where p does not equal 3, is a prime number, then p is neither divisible by 4 nor divisible by 3. (Alternatively, prove that if p is divisible by 4 or 3, then 2^p - 1 is divisible by some number other than positive/negative itself or positive/negative 1.) \n" ); document.write( "

Algebra.Com's Answer #55233 by Edwin McCravy(20055) $\"\"$ $\"About$

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We use the factor theorem, which is the identity: \r\n" );
document.write( "(+ ЗЗЗ +  + ЗЗЗ + )\r\n" );
document.write( "Suppose p is divisible by 4, then there exists \r\n" );
document.write( "positive integer q such that p=4q, then \r\n" );
document.write( " =\r\n" );
document.write( "(+ ЗЗЗ +  + ЗЗЗ + ) =\r\n" );
document.write( "15(+ ЗЗЗ +  + ЗЗЗ + ) so \r\n" );
document.write( " is either 15 (when q=1) or divisible \r\n" );
document.write( "by 15, and in either case is not prime.\r\n" );
document.write( "\r\n" );
document.write( "For the case when p is divisible by 3, then there exists \r\n" );
document.write( "positive integer q such that p=3q. Do the same as\r\n" );
document.write( "above and you have 7 where the 15 is above and \r\n" );
document.write( "is not prime unless it equals 7, i.e., unless q=1, i.e.,\r\n" );
document.write( "unless p=3, but that is ruled out in the hypothesis.\r\n" );
document.write( "Edwin

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