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August 26th, 2012, 09:45 PM   #1
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Modular Arithmetic

Can anyone shed a little light on this problem?

Prove that if is a multiple of 4 then

It may help to know that

The solution I was given was to use induction
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August 26th, 2012, 10:11 PM   #2
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Re: Modular Arithmetic

I'm not sure about your notation, but I am guessing you are to prove that:

where

Is this correct?
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August 27th, 2012, 09:34 AM   #3
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Re: Modular Arithmetic

Hello, aaron-math!

Quote:


















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August 27th, 2012, 09:51 AM   #4
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Re: Modular Arithmetic

A folksier version:

Any number that ends in 1 = 1 mod 10 = 1 mod 5

Any number that ends in 1 x any number that ends in 7 ends in 7. (7^1, 7^5, 7^9...)
Any number that ends in 7 x any number that ends in 7 ends in 9. (7^2, 7^6, 7^10...)
Any number that ends in 9 x any number that ends in 7 ends in 3. (7^3, 7^7, 7^11...)
Any number that ends in 3 x any number that ends in 7 ends in 1. (7^4, 7^8, 7^12...)
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