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.

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