Tanto si el número es par como si es impar, quiero entender por qué cambia la fórmula.

It means whether ... or ... or regardless of whether ....

So:

Tanto si el número es par como si es impar
= Whether the number is even or odd

It is a fixed Spanish pattern used to present two alternatives.

Because this is a correlative structure in Spanish:

tanto si + option 1 + como si + option 2

Spanish normally repeats si before both alternatives. That is just how the pattern is built.

So you say:

Tanto si es par como si es impar

not:

Tanto si es par como es impar

Because here como si is part of the whole structure tanto si ... como si ....

That is different from the separate expression como si meaning as if, which normally takes the subjunctive:

Habla como si supiera todo
= He speaks as if he knew everything

But in your sentence, como si is not as if. It is simply the second half of whether ... or ....

Because the sentence is talking about a real classification: a number is either even or odd. Spanish normally uses the indicative after si in this kind of structure.

So:

si el número es par
si es impar

Both are treated as real possibilities, not imagined or unreal ones.

If you used sea, you would usually be using a different structure, for example:

ya sea par o impar

That is a different pattern from tanto si ... como si ....

Because Spanish often leaves out repeated words when they are already clear from context.

The full idea is:

Tanto si el número es par como si el número es impar

But repeating el número sounds unnecessary, so Spanish naturally shortens it to:

Tanto si el número es par como si es impar

This is very common.

Because Spanish often uses the definite article with a singular noun when speaking about something in a general or contextual way.

Here el número means the number being discussed.

English and Spanish do not always use articles in the same way, so this is something learners often need to get used to.

Because after ser, Spanish often uses a noun or adjective directly to describe a category or property.

So:

es par
es impar

This works like:

es importante
es médico

The words par and impar are acting as classifications or properties here, so no article is needed.

Because this is an indirect question:

quiero entender por qué cambia la fórmula
= I want to understand why the formula changes

In Spanish:

• por qué = why
• porque = because

So here you need por qué, with two words and an accent on qué.

Because por qué cambia la fórmula is an indirect question about something presented as a real fact: the formula changes, and the speaker wants to know why.

So Spanish uses the indicative:

por qué cambia

The subjunctive cambie would need a different kind of trigger or meaning.

Quiero entender means I want to understand. It suggests the speaker wants real comprehension, not just the answer.

Compare:

• quiero saber por qué = I want to know why
• quiero entender por qué = I want to understand why

So entender sounds a bit deeper: the speaker wants to grasp the reason or logic behind the change.

It is the normal punctuation here because the sentence begins with a fairly long introductory clause:

Tanto si el número es par como si es impar, ...

The comma helps separate that opening clause from the main clause:

quiero entender por qué cambia la fórmula

Without the comma, the sentence would still be understandable, but the comma is the standard and clearer choice.

Yes. A few natural alternatives are:

Sea el número par o impar, quiero entender por qué cambia la fórmula.

Ya sea par o impar, quiero entender por qué cambia la fórmula.

These mean almost the same thing. The original version with tanto si ... como si ... is perfectly natural and emphasizes the two alternatives clearly.