document.write( "Question 1089031: f(n) = n^5 - n , n = N , then f(n) is divisible by \n" ); document.write( "

Algebra.Com's Answer #703363 by Fombitz(32388) $\"\"$ $\"About$

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$\"f%28n%29=n%5E5-n\"$
\n" ); document.write( " $\"f%28n%29=n%28n%5E4-1%29\"$
\n" ); document.write( " $\"f%28n%29=n%28n%5E2-1%29%28n%5E2%2B1%29\"$
\n" ); document.write( " $\"f%28n%29=n%28n%2B1%29%28n-1%29%28n%5E2%2B1%29\"$
\n" ); document.write( "So when $\"n=N\"$ ,
\n" ); document.write( " $\"f%28N%29=N%28N%2B1%29%28N-1%29%28N%5E2%2B1%29\"$
\n" ); document.write( "Then $\"f%28N%29\"$ is divisible by,
\n" ); document.write( " $\"N\"$ , $\"N%2B1\"$ , $\"N-1\"$ , and $\"N%5E2%2B1\"$ . \n" ); document.write( "

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