How many integer solutions are there to …
2020年10月17日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
elementary number theory - Find $x$ so $x^{31}\equiv 2 …
2016年10月6日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
modular arithmetic - Solving the congruence $7x + 3 = 1 \mod 31 ...
2019年10月3日 · $7x + 3 \equiv 1 \pmod{31} \text{ iff } 7x\equiv -2\pmod{31}$ Also, when working with a linear congruence you might as well get rid of any minus signs. So, you want to solve
Proof that $x^3+y^4=z^{31}$ has infinitely many solutions
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What are the common solutions of $x^2+y=31$ and $y^2+x=41$?
$\begingroup$ Note, if you graph $(31-x^2)^2$ again $41-x$ and $41$, you'll see that the constant line and the $41-x$ line are dominated by the large swing in the $(31-x^2)$, so the solutions to $(31-x^2)^2=41$ give you a good "guide" of …
Solutions to $x+y+z=31$ and $x+2y+3z=41$ - Mathematics Stack …
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Proving that $x^3-9$ is irreducible in $\\mathbb{F}_{31}[x]$
2018年2月28日 · I am attempting to solve part (b) of problem 4.2 in Chapter 12 of Artin's Algebra textbook. I have already solved part (a).
Find all real triples $(x,y,z)$ such that: …
2017年8月12日 · Find all real triples $(x,y,z)$ such that: $x^2+1=2y,y^2+1=2z,z^2+1=2x$. Can it be solved avoiding equations of orders higher than 2?
find all the integral solution for $y^2 + 31 = x^3$
2021年4月1日 · $\begingroup$ @Martund There are so many proofs given at this site. For a reference, see for example the table and the references here, where $31$ is listed as having no solution.
Is $x^3-9$ irreducible over the integers mod 31?
To work modulo a small prime like $31$ is not at all tedious. Just start with some positive integer and write down its powers successively, reducing modulo $31$ each time. With luck, you will have chosen a primitive residue, and you get all $30$ nonzero residues. This gives you a log table for multiplication modulo $31$.