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# M28-26

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Math Expert
Joined: 02 Sep 2009
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Math Expert
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Own Kudos [?]: 643201 [8]
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Boycot wrote:
My apologies for a simple question, but how is it possible to prove that odd^2 divided by 4 always yields the reminder of 1?

Is it correct based on (o/2)*(o/2)=(q*2+1)(q*2+1), so after multiplication we can conclude that R=1

Or based on (odd^2-1+1)/4, where odd^2-1 is always divisible by 4

Or is it a rule that i missed?

My concern aroused cause originally i came to the conclusion base on several numbers substitution.

An odd number can be represented as 2k + 1 --> (2k + 1)^2 = 4k^2 + 4k + 1 --> first two terms are divisible by 4, so the remainder would come only from the third term --> 1 divided by 4 yields the remainder of 1.

Check it with numbers:
1^2 = 1 yields the remainder of 1 when divided by 4;
3^2 = 9 yields the remainder of 1 when divided by 4;
5^2 = 25 yields the remainder of 1 when divided by 4;
...

Hope it's clear.
Math Expert
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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