document.write( "Question 519617: Hello,
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\n" ); document.write( "\n" ); document.write( "The difference of the squares of two positive integers which differ by 2 is a perfect square n^2 . Find all possible values of n.\r
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Algebra.Com's Answer #345721 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Two positive integers that differ by 2 can always be written as k+1 and k-1,\r\n" );
document.write( "k>=2\r\n" );
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document.write( "The difference of their squares is\r\n" );
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document.write( "(k+1)²-(k-1)² = 4k  \r\n" );
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document.write( "4k will be a perfect square if and only if k is a perfect square.\r\n" );
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document.write( "So let k = m²\r\n" );
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document.write( "Then (k+1)²-(k-1)² = 4k = 4m² = (2m)² = n².  Thus n = 2m\r\n" );
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document.write( "I.e., n can be and can only be any even positive integer.\r\n" );
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document.write( "Edwin
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