document.write( "Question 1079492: What is the sum of the two smallest distinct prime factors of 2^{27} + 3^{27}? \n" ); document.write( "

Algebra.Com's Answer #693817 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "What is the sum of the two smallest distinct prime factors of 2^{27} + 3^{27}?'
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\n" ); document.write( "\n" ); document.write( "Answer. This sum is 5 + 7 = 12.\r
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document.write( "1.  It is clear that 2 is not a factor of  .\r\n" );
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document.write( "2.  It is clear that 3 is not a factor of  .\r\n" );
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document.write( "3.    has the factor (2 + 3) = 5  since    has this well known decomposition in the product of these factors:\r\n" );
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document.write( "     = \r\n" );
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document.write( "    Thus the first smallest prime factor of the sum    is 5.\r\n" );
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document.write( "4.    has the factor  = 35  since    can be factored in this way:\r\n" );
document.write( "   \r\n" );
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document.write( "      =  =  = \r\n" );
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document.write( "    and (8+27) = 35 is multiple of 7,  so the second smallest prime divisor of this sum is 7 (next after 5).\r\n" );
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document.write( "5.  Therefore, 5 + 7 = 12 is the answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On factoring binomials $\"x%5En-a%5En\"$ and $\"x%5En%2Ba%5En\"$ see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Factoring the binomials    $\"x%5En-a%5En\"$ \r
\n" ); document.write( "\n" ); document.write( "    - Factoring the binomials    $\"x%5En%2Ba%5En\"$ for odd degrees\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "\"Factoring binomials $\"x%5En-a%5En\"$ and $\"x%5En%2Ba%5En\"$ \".\r
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