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Square of an Odd (Posted on 2002-10-06) Difficulty: 2 of 5
Take any odd number and square it. It will invariably be a multiple of 8 plus 1. So (odd)^2=8n+1 where n is an integer. Show why this is always so. Also show what the pattern for n is.

See The Solution Submitted by martyn    
Rating: 3.1333 (15 votes)

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Solution Part 1,The formula for n | Comment 10 of 20 |
We last proved that for the odd number 2m+1,n=m^2/2+m/2,which is the formula for the mth triangular number.
Basically,if an odd number is 2m+1,then its square is 8n+1,where n is the mth triangular number.
  Posted by Tim Axoy on 2003-03-26 02:24:55
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