(i) Consider
(ii) Assume the last digit of N is 1. That is, . Use the fact that .
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 ...
That's great . 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