document.write( "Question 181675: A student claims that every prime greater than 3 is a term in the arithmetic sequence who nth term is 6n+1 or in the arithmetic sequence whose nth term is 6n-1. Is this true? If so why? \n" ); document.write( "

Algebra.Com's Answer #136322 by Edwin McCravy(20060) $\"\"$ $\"About$

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A student claims that every prime greater than 3 is a term in the arithmetic sequence who nth term is 6n+1 or in the arithmetic sequence whose nth term is 6n-1. Is this true? If so why?
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document.write( "Look at those two arithmetic sequences:\r\n" );
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document.write( "The arithmetic sequence whose nth term is 6n+1 is 7,13,19,25,31,37,...\r\n" );
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document.write( "The arithmetic sequence whose nth term is 6n-1 is 5,11,17,23,29,35,...\r\n" );
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document.write( "One of the other of those two progressions contains every odd number\r\n" );
document.write( "greater than 3, which is not a multiple of 3.  And since every prime \r\n" );
document.write( "number greater than 3 is odd, and is not a multiple of 3, it must be \r\n" );
document.write( "true for every prime number greater than 3.\r\n" );
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document.write( "Quod Erat Demonstrandum\r\n" );
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document.write( "Edwin

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