document.write( "Question 1209235: Find the number of ordered pairs (m,n) of integers that satisfy
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Algebra.Com's Answer #847888 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the number of ordered pairs (m,n) of integers that satisfy
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document.write( "Transform the given equation this way\r\n" );
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document.write( "    mn - 3m - 3n + 9 = 26,\r\n" );
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document.write( "    (n-3)*(m-3) = 26.\r\n" );
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document.write( "So, n-3 and m-3 are divisors of 26.\r\n" );
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document.write( "There are 4 different decompositions of 26 into the product of positive integer numbers\r\n" );
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document.write( "    8 = 1*26 = 2*13 = 13*2 = 26*1\r\n" );
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document.write( "It gives 4 different pairs (m,n).         // Since the problem does not ask to find them,\r\n" );
document.write( "                                             I will not find them.\r\n" );
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document.write( "There are 4 different decompositions of 26 into the product of negative integer numbers\r\n" );
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document.write( "    26 = (-1)*(-26) = (-2)*(-13) = (-13)*(-2) = (-26)*(-1).\r\n" );
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document.write( "It gives 4 other different pairs (m,n).   // Since the problem does not ask to find them,\r\n" );
document.write( "                                             I will not find them.\r\n" );
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document.write( "In all, there are 4+4 = 8 different pairs of integer numbers, satisfying the given equation.\r\n" );
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