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[spamegg1]

Welcome! 🎉

[ahmedhalimx]

I think there is a mistake In Chapter 3, Exersice Set 3.2, Question 34 (a).
PDF solution: If n is not divisible by any prime number from 2 through √n, then n is not prime.
My Solution: If n is divisible by any prime number from 2 through √n, then n is not prime.
Which is right?

[spamegg1]

You are correct; this was fixed just recently so you might want to get the latest release.

[cything]

Is 3.3.41(g) question incorrect?

[spamegg1]

I don't think so, why is it incorrect? Can you explain?

[cything]

You have it as $\exists x \in \mathbb{R}$ such that $\forall y \in \mathbb{R}$, $y < x$ (Epp.tex#9181). In the book the question is $\forall x \in \mathbb{R}^+, \exists y \in \mathbb{R}^+$ such that $y<x$.

[elfaidi-ghassen]

I'm having a hard time understanding 4.7.16, can you help me?
in the solution, it says $b > a$ because $b^2 - a^2 = 4 > 0$, I don't understand why that's true in this exercise, I feel I'm missing something. Also, the unique prime factors of 4 are $2 . 2$ and $4 . 1$
but, don't we need to also verify the cases? like $(b + a) = -2$ and $(b - a) = -2$?

[spamegg1]

Yes you are right, it would only give us $|b| > |a|$.
I must have implicitly assumed that $a,b$ are positive.

We can actually assume $a,b$ are positive without loss of generality,
because $b^2 = (-b)^2$ and $a^2 = (-a)^2$ so if they are negative,
they can be replaced by $-b, -a$ without affecting anything.

I'll add the "WLOG" to the proof, thanks!