document.write( "Question 130501: I am struggling with this question, can someone help?
\n" ); document.write( "thanks so much.
\n" ); document.write( " Select any odd integer greater than 1, square it, and then subtract 1. Is the result evenly divisible by 8? Prove that this procedure always produces a number divisible by 8. (Suggestion: Any odd integer greater than 1 can be expressed as 2n + 1, where n is a natural number.) \n" ); document.write( "
Algebra.Com's Answer #95324 by amine(11)\"\" \"About 
You can put this solution on YOUR website!
a odd number is x=2n+1
\n" ); document.write( "then x*x=(2n+1)(2n+1)=4n^2 + 4n + 1\r
\n" ); document.write( "\n" ); document.write( "then x^2-1=4n^2 + 4n
\n" ); document.write( " =4n(n+1)\r
\n" ); document.write( "\n" ); document.write( "the n will be a odd or a pair number\r
\n" ); document.write( "\n" ); document.write( "1)now if the n is a odd number then n=2m+1 will m>=0 then n+1=2m+2 ==>
\n" ); document.write( "n+1= 2(m+1)\r
\n" ); document.write( "\n" ); document.write( "with this
\n" ); document.write( "x^2-1=4n(n+1)
\n" ); document.write( " =4n(2(m+1)) = 8n(m+1) then divisible by 8\r
\n" ); document.write( "\n" ); document.write( "2) if the n is a pair number then n=2m
\n" ); document.write( "x^2-1=4n(n+1)=8m(n+1)
\n" ); document.write( "then divible by 8\r
\n" ); document.write( "\n" ); document.write( "cheers \n" ); document.write( "
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