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January 22nd, 2009, 08:07 PM   #1
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so confused here...

ok this is the problem/question

Show that the square of an odd integer is of the form 8k +1 for some k in a set of integers.


so like....how do u even start this problem????
all i know is that i need to do a proof
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January 23rd, 2009, 05:08 AM   #2
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Re: so confused here...

Try each of the possibilities mod 8. There are only 4.
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January 23rd, 2009, 07:08 AM   #3
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Re: so confused here...

Steps:
1. Any odd integer has form O = 2k + 1.
2. Square of it is O^2 = 4k(k + 1) + 1.
3. If k = 2n, then O^2 = 8n(2n + 1) + 1 = 8m + 1
4. If k = 2n + 1, then O^2 = 8(n + 1)(2n + 1) + 1 = 8p + 1
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