document.write( "Question 123516This question is from textbook Discrete Mathematics
\n" ); document.write( ": Prove that there is a positive integer that can be written as the sum of squares of positive integers in two different ways. \n" ); document.write( "
Algebra.Com's Answer #90637 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Prove that there is a positive integer that \r\n" );
document.write( "can be written as the sum of squares of \r\n" );
document.write( "positive integers in two different ways.\r\n" );
document.write( "\r\n" );
document.write( "There are lots of such positive integers.\r\n" );
document.write( "65 and 85 are the two smallest examples:\r\n" );
document.write( "\r\n" );
document.write( "65 = 1 + 64 = 1² + 8² \r\n" );
document.write( "65 = 16 + 49 = 4² + 7²\r\n" );
document.write( "\r\n" );
document.write( "85 = 4 + 81 = 2² + 9²\r\n" );
document.write( "85 = 36 + 49 = 5² + 7² \r\n" );
document.write( "\r\n" );
document.write( "Here's one that can be written as the \r\n" );
document.write( "sum of squares in three different ways:\r\n" );
document.write( "\r\n" );
document.write( "325 = 1 + 324 = 1² + 18²\r\n" );
document.write( "325 = 36 + 289 = 6² + 17²\r\n" );
document.write( "325 = 100 + 225 = 10² + 15²\r\n" );
document.write( "\r\n" );
document.write( "Here's one that can be written as the \r\n" );
document.write( "sum of squares in four different ways:\r\n" );
document.write( "\r\n" );
document.write( "1105 = 16 + 1089 = 4² + 33² \r\n" );
document.write( "1105 = 81 + 1024 = 9² + 32²\r\n" );
document.write( "1105 = 144 + 961 = 12² + 31²\r\n" );
document.write( "1105 = 529 + 576 = 23² + 24²\r\n" );
document.write( "\r\n" );
document.write( "Here's one that can be written as the \r\n" );
document.write( "sum of squares in five different ways:\r\n" );
document.write( "\r\n" );
document.write( "5525 = 49 + 5476 = 7² + 74²\r\n" );
document.write( "5525 = 196 + 5329 = 14² + 73²\r\n" );
document.write( "5525 = 484 + 5041 = 22² + 71²\r\n" );
document.write( "5525 = 625 + 4900 = 25² + 70²\r\n" );
document.write( "5525 = 1681 + 3844 = 41² + 62²\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );