I am asking how one can motivate finding the proof to this problem. An understanding of the problem should also provide some insight into why the solution has a certain approach to it, and motivate why someone should consider such a solution.

Currently, this solution is like "magic", where while the individual steps are explained, it is not clear why we chose them, or why these steps work. For example, why do we look at \( p\equiv 1 \pmod{8} \)? What is it about \( n^2 + 1 \) that tells us about prime divisors of the form \( p \equiv 1 \pmod{8} \)?

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestSince Nobody posted the proof here is the proof:

Log in to reply

What is the motivation behind this? How can one go about approaching this proof?

Log in to reply

Well it helps in school unlike from brilliant here we have 3 chances.

Log in to reply

I am asking how one can motivate finding the proof to this problem. An understanding of the problem should also provide some insight into why the solution has a certain approach to it, and motivate why someone should consider such a solution.

Currently, this solution is like "magic", where while the individual steps are explained, it is not clear why we chose them, or why these steps work. For example, why do we look at \( p\equiv 1 \pmod{8} \)? What is it about \( n^2 + 1 \) that tells us about prime divisors of the form \( p \equiv 1 \pmod{8} \)?

Log in to reply