document.write( "Question 449516: No matter what two integers I choose, their squares cannot differ by\r
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\n" ); document.write( "D) 2005\r
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Algebra.Com's Answer #309574 by richard1234(7193) $\"\"$ $\"About$

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If a and b are the integers, with

|b|\">, then\r
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\n" ); document.write( "\n" ); document.write( "We can factor each of 2002, 2003, 2004, 2005. We must note that if there exist factors a-b and a+b with (a-b)(a+b) = 2002, ..., 2005, and the sum of these two factors is even (equal to 2a), then a and b are integers.\r
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\n" ); document.write( "\n" ); document.write( "However, all factorizations of 2002 have an odd \"sum\" (e.g. 1*2002, 2*1001, 7*286, etc., in which their sums are 2003, 1003, 293). These numbers cannot be equal to twice an integer, so 2002 is the only impossible choice. \n" ); document.write( "

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