document.write( "Question 1135584: Integers that can be expressed as the sum of three squares in three different ways? \n" ); document.write( "

Algebra.Com's Answer #753228 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "the sum of squares $\"3n\"$ procedure finds all $\"+a\"$ , $\"b\"$ , $\"c\"$ such that $\"n+=+a%5E2+%2B+b%5E2+%2B+c%5E2\"$
\n" ); document.write( "It works by repeatedly invoking sum of squares on $\"n-i%5E2\"$ where $\"i\"$ is incremented after each iteration from $\"1\"$ to square root of $\"n%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Do you want *exactly* $\"3\"$ ways, or *at least* $\"3\"$ ways? \r
\n" ); document.write( "\n" ); document.write( "Assuming order isn't considered, and assuming you want it $\"exactly\"$ in $\"3+\"$ ways, here are a few numbers: \r
\n" ); document.write( "\n" ); document.write( " $\"54\"$ , $\"66\"$ , $\"81\"$ , $\"+86\"$ , $\"89\"$ , $\"99\"$ , $\"+101\"$ , $\"110\"$ , $\"114\"$ , $\"126\"$ , $\"131\"$ , $\"149\"$ , $\"+150\"$ , $\"162\"$ , $\"166\"$ , $\"173\"$ , $\"174\"$ , $\"+179\"$ , $\"182\"$ , $\"185\"$ , $\"186\"$ , $\"216\"$ , $\"219\"$ , $\"221\"$ , $\"222\"$ , $\"225\"$ , $\"227\"$ , $\"233\"$ , $\"237\"$ , ... \r
\n" ); document.write( "\n" ); document.write( "Example: \r
\n" ); document.write( "\n" ); document.write( " $\"182+=+1%5E2+%2B+9%5E2+%2B+10%5E2\"$
\n" ); document.write( " $\"182+=+2%5E2+%2B+3%5E2+%2B+13%5E2\"$
\n" ); document.write( " $\"182+=+5%5E2%2B+6%5E2+%2B+11%5E2\"$ \r
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