Trouble with a proposition

Proposition 5.18 (An introduction to mathematical cryptography)

Let n be a positive integer and let which means that Then we can always write

With and at most of the nonzero.

So say if we have n=61 then then which is definitly not greater than 61. So the first line of the proposition is not correct. Where on earth am i going wrong!! I must be missing something?

Any insight would be greatly appreciated,

cheers

Re: Trouble with a proposition

Quote:

Originally Posted by

**liedora** Proposition 5.18 (An introduction to mathematical cryptography)

Let n be a positive integer and let

which means that

Then we can always write

With

and at most

of the

nonzero.

So say if we have n=61 then

In fact, the log (to base 2) of 61 is 5.93..., so its integer part is 5, and , not 5.
then

which is definitely not greater than 61. So the first line of the proposition is not correct. Where on earth am i going wrong!! I must be missing something?

It doesn't explicitly say so, but the context makes it clear that the logs here must be to base 2.

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