document.write( "Question 501342: If two numbers are odd, then is their sum even? \n" ); document.write( "

Algebra.Com's Answer #338491 by Mr_Mathman(5) $\"\"$ $\"About$

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Yes. Here is a proof\r
\n" ); document.write( "\n" ); document.write( "First a definition:
\n" ); document.write( "multiplying any integer by two gives an even number and adding one to that gives an odd number\r
\n" ); document.write( "\n" ); document.write( "Let j=2m+1 and k=2n+1 where m and n are integers.
\n" ); document.write( "Add j and k
\n" ); document.write( "j+k=2m+1+2n+1=2m+2n+2=2(m+n)+2
\n" ); document.write( "now we can let l=m+n
\n" ); document.write( "and j+k=2l+2
\n" ); document.write( "From the definition we know that multiplying any integer by two gives an even number and adding one to that gives an odd number.
\n" ); document.write( "It should be clear that adding two instead results in an even number.\r
\n" ); document.write( "\n" ); document.write( "QED \n" ); document.write( "

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