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.
(In reply to no solution?
Even when you include a solution when you submit the problem, it is not posted for a few days. This allows you to make corrections or additions (for example in one of my puzzles, one of the comments had a more elegant solution than I had, so I added anacknowledgement), and gives the rest of us "encouragement" not to just give up and "look in the back of the book." There should be a link that says "This is your problem," which will allow you to see and change the solution you submitted.
Posted by TomM
on 2002-10-06 17:33:36