Tagged Questions
0
votes
0answers
30 views
How do I find the set of integers solving a system of equations that contain outliers?
I have a system of $s$ equations that should (but won't) all equal some real unknown scalar value, $x$:
$x = v_1*k_1 + a_1*k_1*m = v_2*k_2 + a_2*k_2*m = ... = v_s*k_s + a_s*k_s*m$
where,
$k_i$ are ...
2
votes
1answer
55 views
How many solutions to prime = $2 b^2 c^2 + 2 c^2 a^2 + 2 a^2 b^2 - a^4 - b^4 - c^4$
Let $a,b,c$ be integers, no sign restriction.
Let $p$ be a given prime.
How to find the number of solutions to $p = 2 b^2 c^2 + 2 c^2 a^2 + 2 a^2 b^2 - a^4 - b^4 - c^4$ ?
Note, from Heron's ...
3
votes
3answers
119 views
How many solutions to prime = $a^3+b^3+c^3 - 3abc$
Let $a,b,c$ be integers.
Let $p$ be a given prime.
How to find the number of solutions to $p = a^3+b^3+c^3 - 3abc$ ?
Another question is ; let $w$ be a positive integer. Let $f(w)$ be the number of ...
1
vote
2answers
71 views
How many solutions to prime = $(d^2-2ad+b^2-2ab+2a^2)(d^2-2cd+2c^2-2bc+b^2)$?
Let $a,b,c,d$ be integers $>-1$.
Let $p$ be a given prime.
How to find the number of solutions to $p = (d^2-2ad+b^2-2ab+2a^2)(d^2-2cd+2c^2-2bc+b^2)$ ?
I assumed that this polynomial above does not ...
0
votes
1answer
134 views
How to solve $ x^2+4x+2 \equiv 0 \pmod{49}$
How to decompose equations below and then solve
1)$$ 2x^3 + 7x - 4 \equiv 0 \pmod{25} $$
2)$$ x^2+4x+2 \equiv 0 \pmod{49}$$
Thank you.
1
vote
2answers
160 views
Solving an equation in modular arithmetic
Given $A, B, C$ positive integers, $B < C,$
I would like some thoughts about (possibly efficient) ways to find the
smallest integer $X$, where $0 < X < C$, such that:
$$A X + B \pmod{C - ...
4
votes
2answers
54 views
Deciding if a univariate quartic has a solution mod p
I have an equation in $x$ and I would like to determine if it has any solutions modulo a large prime $p$. Suppose $p$ is large enough that I can factor numbers up to $p$, but I cannot test all values ...
1
vote
1answer
67 views
Solving $a + b x = c y$ in the integer domain for general $a$
I have the following equation:
$\frac{a + b x}{c} \in \mathbb{N}$ where $a,b,c,x \in \mathbb{N}$.
and I want to find all x that satisfy these requirements. This should be the same as:
$a + b x = c ...
2
votes
0answers
31 views
Solving $key=(\sum_{K=0}^n\frac{1}{a^K})\mod m$ with High limits
I was solving this equation:-
$$key=(\sum_{K=0}^n\frac{1}{a^K})\mod m$$
Given
$$ 1,000,000,000 < a, n, m \; < 5,000,000,000 $$
$$ a, m \; are \;coprime $$
I solved it bruteforcely but it ...
1
vote
2answers
68 views
Enumerating all $x$ such that $b^n$ divides $x^2-x$
Given $b$ and $n$, I need to efficiently enumerate all integers $x$ (and $k$) such that:
$$x^2-x=kb^{n}$$
$$x∈⟦b^{n-1},b^n-1⟧$$
I simply don't know how to proceed. I tried the naive quadratic ...
2
votes
4answers
435 views
solve $100x - 23y = -19$
I need help with this equation $$100x - 23y = -19.$$ When I plug this into Wolfram|Alpha, one of the integer solutions is $x = 23n + 12$ where $n$ is a subset of all the integers, but I can't seem to ...
