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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 induction does it | Comment 12 of 20 |
induction is the shortest proof:
for n=1 8*1+1 ok

given the formula holds for n

for n+2 (next odd) 8*( n+2)+1= (8*n+1)+16

qed
ady
  Posted by Ady TZIDON on 2004-03-04 03:30:15
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