document.write( "Question 579440: a^2 - b^2 = 391. Find the number of Integral Solutions?\r
\n" ); document.write( "\n" ); document.write( "e.g. x + y = 2 has infinite numbers of Integral Solution. \n" ); document.write( "
Algebra.Com's Answer #371016 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor just wrote 4, which is wrong, with\r\n" );
document.write( "no explanation at all.  I have no idea why he would\r\n" );
document.write( "do that.\r\n" );
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document.write( "Here is the explanation and answer:\r\n" );
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document.write( "       aČ - bČ = 391\r\n" );
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document.write( "(a - b)(a + b) = 391\r\n" );
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document.write( "The only ways to factor 391 are\r\n" );
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document.write( "        391·1\r\n" );
document.write( "and      23·17\r\n" );
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document.write( "We will first consider a and b to be positive\r\n" );
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document.write( "So we have either the system\r\n" );
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document.write( "\"system%28a-b=1%2Ca%2Bb=391%29\" which has solution a=196, b=195\r\n" );
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document.write( "or\r\n" );
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document.write( "\"system%28a-b=17%2Ca%2Bb=231%29\"  which has solution a=20, b=3\r\n" );
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document.write( "Since a and b are squared in the original equation, we may \r\n" );
document.write( "choose either sign, so these are the integral solutions:\r\n" );
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document.write( "1. a = 196, b = 195\r\n" );
document.write( "2. a = 196, b = -195\r\n" );
document.write( "3. a = -196, b = 195\r\n" );
document.write( "4. a = -196, b = -195\r\n" );
document.write( "5. a = 20, b = 3\r\n" );
document.write( "6. a = 20, b = -3\r\n" );
document.write( "7. a = -20, b = 3\r\n" );
document.write( "8. a = -20, b = -3\r\n" );
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document.write( "So there are 8 solutions.\r\n" );
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document.write( "Edwin

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