document.write( "Question 1114882: If m and k are integers, what are all the solutions to the equation $\"9%287%5Ek%2B7%5E%28k%2B2%29%29=+5%5E%28m%2B3%29%2B5%5Em\"$ \n" ); document.write( "

Algebra.Com's Answer #729799 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "If m and k are integers, what are all the solutions to the equation $\"9%287%5Ek%2B7%5E%28k%2B2%29%29=+5%5E%28m%2B3%29%2B5%5Em\"$
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document.write( " =   ====>\r\n" );
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document.write( " = \r\n" );
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document.write( " =   ====>   Divide both sides by 9  ====>\r\n" );
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document.write( " =   ====>\r\n" );
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document.write( " =   ====>  Comparing prime factors and their degrees and using the theorem on uniqueness \r\n" );
document.write( "                         of decomposition integers into the product of their prime factors\r\n" );
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document.write( "Answer.  m = 2,  k = 1.\r\n" );
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