Question

Find the canonical decomposition of2^9-1​

Answer 1

Answer

x∼y⇔f(x)=f(y).

So in this case, you can show that the relation is x∼y⇔e2iπx=e2iπy⇔x≡ymod1

Then your quotient is R/∼={x+Z:x∈R} where x+Z={x+n:n∈Z}.

So q(x)=x+Z and f~(x+Z)=exp(2iπx) (v is like in your question).tion:

Answer 2

Answer: SOLUTION

TO DETERMINE

The canonical decomposition of 2013

CONCEPT TO BE IMPLEMENTED

1. Every integer n > 1 can be expressed uniquely as a product of prime powers

2. If n is an integer. Then n can be written as

Where

EVALUATION

Here the given number is 2013

Now

Which is the required canonical decomposition of 2013

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