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 Jan 27 comment Plaintext attacks: affine cipher @kodlu There is no $c_1$ in that part of the question (the part where $p$ is unknown). Jan 22 answered Is $\mathbb R^3$ subspace of $\mathbb R^4$ Jan 12 comment Negation of injectivity There is no "but" in logic, the negation of "P implies Q" is "P and not Q". Dec 31 awarded Yearling Dec 4 comment Why is this prime a bad choice for the ElGamal cryptosystem? Ask your favourite search engine about the Pohlig-Hellman algorithm. Dec 2 comment Quotient ring $\mathbb{Z}/4\mathbb{Z}$ One thing to remember when working with quotient groups (rings, etc.) is that an element of the quotient structure is a subset of the original structure. Hence one immediately sees that your definition of Z/4Z is off because you define its elements to be integers, when they actually are sets of integers. Dec 1 comment Reference Request for Topics in Group Theory A specialised group theory textbook (as opposed to a general algebra one) will obviously cover it in more depth. I like the book of Roman, but there are many others. Nov 29 comment Uses of vector spaces over $\mathbb Q$ Basically all of classical algebraic number theory, for starters, which was developed to answer questions about the good ol' integers. Nov 22 comment Is there a surjective homomorphism from $Z$ to $\mathbb{Z}_2\times \mathbb{Z}_2$? If there is a surjective homomorphism $f:\mathbf{Z} \to \mathbf{Z}_2 \times \mathbf{Z}_2$, then $\mathbf{Z}/\ker f \cong \mathbf{Z}_2\times \mathbf{Z}_2$. This contradicts something you know about quotients of cyclic groups. Nov 21 comment If $G = \{g_1, … , g_r\}$ is abelian and $a = g_1…g_r$ show that $a^2 = 1$. The elements of $G$ can be sorted in "pairs" of inverses, although some "pairs" will have only one member. Nov 21 comment Understanding issue on demonstrating the congruences theorem "$n$ divides $a-b$" is the usual definition of $a\equiv b \pmod n$, so what's yours? Nov 21 revised Show that the problem of deciding whether a Turing machine prints something is undecidable added 87 characters in body; edited tags; edited title Nov 21 answered Show that the problem of deciding whether a Turing machine prints something is undecidable Nov 20 comment irreducibility of a polynomial over $\mathbb{F}_2$ Berlekamp's algorithm is very good, you don't really need anything better than that. ;) Nov 20 comment Prove F[X]/p(x) contains all roots of p(x) It is in general not true, find a counterexample. Nov 18 comment Let $n\in \mathbb N$. Prove that in $\mathbb{Z}_n$, $(\bar{a}+\bar{b})^2=\bar{a}^2+\bar{2}\bar{a}\bar{b}+\bar{b}^2$ You also do not use that $n$. Nov 16 comment prove why RSA requires the use of distinct primes This is the correct answer. Nov 12 answered Where can I find the paper “Un théorème de compacité” by J. P. Aubin? Nov 7 comment Can you recommend a mathematical logic textbook that is easy to understand? Maybe the author and you have a different definition of "advanced math". Nov 5 comment Solution of Congruence Are you sure you need to find a solution, and not all solutions? In any case, this is called a linear congruence, just Google it, there are countless resources about it.