Hi all,

For these pairs of statements replace ... with . Assume is a positive Integer.

The last digit of is 1 ... The last digit of is 1.

thanks sammy

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- November 12th 2009, 12:57 AMsammy28Proof - Implication signs
Hi all,

For these pairs of statements replace ... with . Assume is a positive Integer.

The last digit of is 1 ... The last digit of is 1.

thanks sammy - November 12th 2009, 01:21 AMDefunkt
(i) Consider

(ii) Assume the last digit of N is 1. That is, . Use the fact that . - November 12th 2009, 01:33 AMBacterius
Try to see if it works from to :

(mod )

So,

Now, , which is equivalent to :

Simple deductions :

(mod )

(mod )

So, (mod )

Therefore, (not formally written but you understand)

Now you try the other way round ( to ), and see if it works. Then you will know what symbol to put ... - November 12th 2009, 08:47 AMsammy28
That's great (Hi). This question is in the introduction to proofs in my 'AS' level book and we have not covered modulus yet. It was aimed really at using the correct implication sign.

I could write out the first few terms and did see both ended in the digit one, but i couldnt work out how to give it a proof.

I can understand why terms 11, 21, 31, 41 would result in , and that the terms squared would also be but does ?

sorry if this is dumb question.

sammy - November 12th 2009, 10:51 AMDefunkt
Hi sammy