document.write( "Question 475361: prove that a perfact number can be written as a sum of (2^n)-1 consicutine numbers for some n. \n" ); document.write( "
Algebra.Com's Answer #326407 by richard1234(7193)\"\" \"About 
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First, we have to assume that all perfect numbers N can be written as for positive integer k.\r
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\n" ); document.write( "\n" ); document.write( "Let m, m+1, ..., (m+2^n)-2 be the (2^n) - 1 consecutive numbers, in which their sum is\r
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\n" ); document.write( "\n" ); document.write( "We want to show that all perfect numbers N can be expressed in this form. However, if we set m = 1 the solution becomes trivial.\r
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\n" ); document.write( "\n" ); document.write( "Alternatively, we can let in which N becomes the sum of the first (2^k) - 1 integers. \n" ); document.write( "
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