0
votes
2answers
16 views

Defining and expressing as a system of two equations. Is my answer good?

We wish to spend $\$164.00$ by purchasing $10$ books, some costing $\$15.00$ and other $\$17.00$. How many books of each price do we buy? My answer: let $x$ = number of books costing $\$15.00$ and ...
0
votes
1answer
32 views

What is the value of $a + b + c + d$ if the following equation holds?

If $a, b, c$ and $d$ are positive integers less than $7$ and $$a(7)^3 + b(7)^2 + c(7) + d = 901$$ What is the value of $a + b + c + d$? Is it related to consum of roots and product of roots?
-1
votes
2answers
43 views

Reminder of equation

I have a simple(maybe too simple) question - how to find the reminder of equation? For example: $(85^{74}+17^{95})^{15} \equiv \ ? \ (mod\ 13)$ I know that it is something simple, but I couldn't ...
0
votes
1answer
11 views

Solve the comparison

I have difficulties with these type of problems: Solve the comparison: $\displaystyle67x + 17 \equiv 0\pmod{28}.$ I'm sure it is something very simple but I'm stuck on it more than $2$ hours :( . ...
2
votes
2answers
56 views

Linear Diophantine equation in two variables with additional constraints

Given, $$aX + bY = c$$ where, $$c > b > a > 0;\quad X, Y > 0;\quad b\nmid c, a\nmid c$$ I want to find out if a solution exists as efficiently as possible (I'm not interested ...
0
votes
1answer
52 views

Stuck solving an equation using the floor operator.

I am not entirely familiar with the equation ninja'ing involving the floor operators. Here is my problem. I need to solve for $x$. Everything is an integer, including $x$: $$ a - 1 = \lfloor {\frac{x ...
6
votes
0answers
154 views

Coefficients in expansion of $(\sqrt[3]{2} - 1)^m$

In trying to solve $a^3 - 2b^3 = 1$ over the integers I came across the need to answer the question: when does $(1+ \sqrt[3]{2} + \sqrt[3]{2}^2)^n$ have no $\sqrt[3]{2}^2$ term in it's expansion (in ...
1
vote
2answers
79 views

TI83+. Math-> Solver. Why does it give different solutions?

Not sure if anyone still uses this one.... Recall the keystrokes: Math 0:Solver Up arrow Enter equation Press ENTER You will now be at a prompt displaying the equation, and a line saying x=### ...
1
vote
1answer
65 views

Two equations & three unknowns (in $\mathbb{Z}$)

I just want to know this system-equation has answer $(x,y,z)$ in Integers Set or not? $a_1x+b_1y+c_1z=d_1$ $a_2x+b_2y+c_2z=d_2$ (in Real Number Set, we just need to check this two plate (plane) ...
0
votes
0answers
69 views

Finding the values of the coefficients from the following two equations.

We have these following two equations, where, and We need to calculate the terms ($A_1,A_2, B_1$ and $B_2$) so that for example, $p_1(R)$ and $A_1 p_1(q) + B_1 p_2(q)$ represent the same ...
1
vote
3answers
98 views

Unique Integer solution of a non-linear equation

How to find the integer solution of the equation $$\frac{m^2 + 2mn + n^2 -3m -n+2}{2}=2$$ I know that there is a unique solution
2
votes
2answers
784 views

Number of non-negative integer solutions for linear equations with constants

How do we find the number of non-negative integer solutions for linear equation of the form: $$a \cdot x + b \cdot y = c$$ Where $a, b, c$ are constants and $x,y$ are the variables ?
1
vote
1answer
60 views

Unique solution to non linear system of equations with boolean coefficients

Say we have a system of $m$ equations of the form: $$a_{11} x_1 + a_{12} x_2 + ... + a_{1n} x_n = p_1$$ $$...$$ $$a_{m1} x_1 + a_{m2} x_2 + ... + a_{mn} x_n = p_m$$ Where the $p_i,x_j \in \mathbb{R}$, ...
1
vote
0answers
49 views

Wrong answer on elementary diophantine equation - why?

Solve the equation and show all possible, non-negative values for X and Y: $5X+4Y=60$ So I wanted to do it like that: $$5X+4Y=60\leftrightarrow0X+4Y=0 \pmod5$$, thus $4Y=5k$ where $k\in Z$. ...
0
votes
3answers
63 views

Is there a squared matrix $A$ sized 2x2 that follows the next criteria?

Is there a squared matrix $A$ sized 2x2 that it's elements $\in \mathbb Z$ so that $$ A^2 = \begin{pmatrix} 2 & 3 \\ 2 & 4 \\ \end{pmatrix} $$
2
votes
2answers
603 views

Finding a basis for the solution space of a system of Diophantine equations

Let $m$, $n$, and $q$ be positive integers, with $m \ge n$. Let $\mathbf{A} \in \mathbb{Z}^{n \times m}_q$ be a matrix. Consider the following set: $S = \big\{ \mathbf{y} \in \mathbb{Z}^m \mid ...
0
votes
1answer
516 views

How to solve Linear Diophantine equations?

I have read about Linear Diophantine equations such as $ax+by=c$ are called diophantine equations and give an integer solution only if $\gcd(a,b)$ divides $c$. These equations are of great importance ...
3
votes
3answers
426 views

Heronian triangle Generator

I'm trouble shooting my code I wrote to generate all Heronian Triangles (triangle with integer sides and integer area). I'm using the following algorithm $$a=n(m^{2}+k^{2})$$ $$b=m(n^{2}+k^{2})$$ ...
0
votes
2answers
319 views

How to find solutions for linear equation?

I want to find the possible values for {$x_i$} for given that I know $y$, {$p_i$} and the sum of $x_i$. In other words, let: $$x_1 \cdot p_1 + x_2 \cdot p_2 + \cdots + x_n \cdot p_n = y$$ ...
4
votes
1answer
184 views

Given $XX^\top=A$, solving for $X$

Not equal to this (my) own question. It's more general, probably more easy than the original question. All of the elements of $X$ and $A$ are integers. $XX^\top=A$ and $A$ is a symmetric matrix. ...
3
votes
0answers
356 views

$XX^t=A$, $X=?$. Where $X \in \{0,1\}^{n \times m}$

The problem: $XX^t=A$, $\quad$ ($X_{ij}\in{0,1}$, $\quad$ $\sum_{j=1}^m x_{ij}=2$), $\quad$ $X=?$ Details: $n,m \in N$ $A \in \{0,1,2\}^{n \times n}$ $X \in \{0,1\}^{n \times m}$ $A$ is a ...
3
votes
1answer
323 views

Non Negative Solutions To a Linear Diophantine?

I have been trying to read a lot of literature concerning the above subject but I've not found anything useful to help my case. Suppose you're given a linear diophantine in $a_1,a_2,\ldots,a_k$ where ...
1
vote
1answer
251 views

Recovering a matrix A from det(A)

I have made up this "fun" problem. The first row of a 3x3 matrix is $(a_{11} a_{12} a_{13})$. The next row consists of the variables $h, g$ and $c$ in any order. The last row are distinct non-zero ...