## 335 Reputation

4 years, 334 days
unemployed
hobo
Perth, Australia

## How to determine if a Set is infinite or...

Maple

As an example question, I am trying to learn a method for assertaining whether a Set with a given predicate is finite or infinite.

For example, is $S$ infinite or finite, if it is defined as:

$$S={\biggl\{k \in \mathbb N:\biggl\lfloor {\frac {{k-1}}{{2} }} \biggr\rfloor-\biggl\lfloor {\frac {{\ln(\pi^{k})}}{{\ln(10)} }} \biggr\rfloor=0}\biggr\}$$

## Proof of totient lemma ...

Maple

Hi I was hoping if someone could mark this proof for a lemma regarding the Euler totient functin for me.

totient_lemma_proof.mw

## Sorry quick question my friend asked me ...

Maple

What is the difference between a divisor and a factor? Like:

with(numtheory):

X := 89733992396903316277681863138688595394562888838833;

S := map(expand, [op(ifactor(X))]):

And we have the singleton of unity for the output of:

divisors(X/(product(S[j], j = 1 .. nops(S))));

and so on:

seq(divisors(X/(product(S[j], j = 1 .. nops(S)-k))), k = 0 .. 3);

but yet if i try

divisors(X);

my computer freezes.

So yes although my friend is somewhat embarassed to not know the difference and needed me to ask for him what the difference between a divisor and a factor is.

Like is it just the uniqueness? ie a factor is one of the terms in the product of a number's prime factorization, where as any number that divides the number is considered to be a divisor?

like for example i can then go:

seq(min(minus(divisors(X/(product(S[j], j = 1 .. nops(S)-k))), {1})), k = 1 .. 10);

X:=X/(131*(139*(151*(163*(173*167)*157)*149)*137)*127)

from the first 10 terms reducing it original number substantially to:

17026820583257598495326242577

and carry this on i dont see why i cant end up with the divisor set that caused my computer to freeze if i just called divisors(X) as I originally did

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## Output not correct for a piecewise...

Maple

Hi, I realise it looks a little messy and I apologize for that, but I wanted to exclude the data pairs for which x or y are equal to 1, and the manner in which I have done has always worked for me thus far, so I would like to understand why or how I should produce output like this in the future thanks in advance.

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