document.write( "Question 1081801: How many ordered pairs of integers (x, y) satisfy y^2 - xy + x = 0? \n" ); document.write( "

Algebra.Com's Answer #695858 by Edwin McCravy(20056) $\"\"$ $\"About$

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How many ordered pairs of integers (x, y) satisfy y^2 - xy + x = 0?
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document.write( "Solve for x\r\n" );
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document.write( "By synthetic division, divide y²+0y+0 by y-1\r\n" );
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document.write( "1 | 1 0 0\r\n" );
document.write( "  |   1 1\r\n" );
document.write( "    1 1 1\r\n" );
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document.write( "Since x and y must be integers, so must ,\r\n" );
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document.write( "and so the denominator y-1 must be 1 or -1.\r\n" );
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document.write( "If the denominator = 1\r\n" );
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document.write( "y-1 = 1\r\n" );
document.write( "  y = 2\r\n" );
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document.write( "So one ordered pair is (x,y) = (4,2)\r\n" );
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document.write( "If the denominator = -1\r\n" );
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document.write( "y-1 = -1\r\n" );
document.write( "  y = 0\r\n" );
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document.write( "So the only other ordered pair is (x,y) = (0,0) \r\n" );
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document.write( "So there are two ordered pairs that satisfy the given equation.\r\n" );
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document.write( "Edwin

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