document.write( "Question 1147347: a,b,c,d are positive integers satisfying (a*b)+(b*c)+(c*d)+(d*a)=36 how many possible values of a+c are there? \n" ); document.write( "
Algebra.Com's Answer #768654 by Edwin McCravy(20056)\"\" \"About 
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document.write( "(a*b)+(b*c)+(c*d)+(d*a)=36\r\n" );
document.write( "We factor:\r\n" );
document.write( "b(a+c)+d(c+a) = 36\r\n" );
document.write( "b(a+c)+d(a+c) = 36\r\n" );
document.write( "   (a+c)(b+d) = 36\r\n" );
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document.write( "a+c and b+d are divisors of 36, which are 1,2,3,4,6,9,12,18,36.\r\n" );
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document.write( "every factor of 36 except 1 and 36, is the sum of two factors of 36.\r\n" );
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document.write( " 2=1+1\r\n" );
document.write( " 3=1+2\r\n" );
document.write( " 4=1+3 =2+2\r\n" );
document.write( " 6=2+4 =3+3\r\n" );
document.write( " 9=3+6\r\n" );
document.write( "12=3+9 =6+6\r\n" );
document.write( "18=6+12=9+9\r\n" );
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document.write( "So there are 7 possible values of a+c.\r\n" );
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document.write( "Edwin
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