1
vote
2answers
48 views

$a^2-b^2 = k$, $ab = l$ for fixed integer $k,l$ when $a,b$ are both integers

Let us fix integers $k,l$. Let all numbers be integers. Now we want integer $a,b$ to satisfy: $$a^2-b^2 = k, \,\,\,2ab = l.$$ We want to maximize the number of possible $(a,b)$. In order to do ...
2
votes
1answer
92 views

Find known number of missing natural numbers

Given a set $S$ of distinct natural numbers, we know that a subset $T$ that is $S$ with at most $k$ number of elements missing. Let $M_k := \big\{m_j\big|d_j = \sum_{i\in T}i^j, j\in ...
1
vote
0answers
44 views

How to express coprimality as a constraint in an optimization problem over integers?

I am currently working with an optimization problem that is defined over a a set of $D$-dimensional integer vectors where each component is bounded by $M$. Let us refer to this optimization problem ...
1
vote
0answers
102 views

Why these two problems lead to same answers?

Suppose these two problems: Problem 1: $$\min_{X,P} \quad\max_{1\leq l\leq L-1} \quad {|\sum_{1\leq i\leq N_p}^{N_p}x_ie^{\frac{2\pi l}{N}p_i}| \over {\sum_{i=1}^{N_p} x_i^2}} \quad \equiv \quad ...
0
votes
1answer
93 views

Converting loop to a closed form expression? [duplicate]

Possible Duplicate: How to convert this loop into a closed form expression? I have the following code in Python ...
0
votes
1answer
26 views

Finding the solutions of $ax+by\le D$

Given parameters $a,b,D$, all integers, I want to find all the integer solutions $(x,y)$ of $ax+by\le D$ Or at least a nice way to characterize them. Also, for a given $R$, it is actually enough for ...