# Tagged Questions

**7**

votes

**2**answers

802 views

### Linear independence of the square roots over Q

Does there exist a real number $a$ such that the numbers $\sqrt{n^2 + a^2}$ (for all natural $n$) are linearly independent over the field of rational numbers? It is evident that $a$ cannot be ...

**0**

votes

**1**answer

340 views

### How to do such a partitioning?

Assume:
$$
P \subseteq \{1,2,\dots,N\},\quad |P| = K, \qquad x \in \mathbb{R}_+^K , \qquad w = e^{-j\frac{2\pi}N}
$$
and,
$$
f(l) = \sum_{i=1}^K \sum_{j=1}^K x_i x_j w^{(p_i-p_j)l}
$$
I am going to ...

**0**

votes

**2**answers

903 views

### Fibonacci Numbers Modulo m [closed]

In the paper "Fibonacci Series Modulo m" by D.D. Wall (found here), there is a table in the Appendix listing values for the function $k(p)$. This function is defined as the period of the Fibonacci ...

**0**

votes

**2**answers

802 views

### non negative integer solutions : Diophantine Equations [closed]

I want to know the exact number of non-negative integer solutions of a1x1+a2x2+...akxk = n ...
I know that it is the co-efficient of x^n in (1-x^a1)^-1 * (1-x^a2)^-1 * ... (1-x^ak)^-1 ...
but whats ...

**18**

votes

**1**answer

1k views

### Number of distinct values taken by x^x^…^x with parentheses inserted in all possible ways

For what positive x's the number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways is not represented by the sequence A000081? Is it exactly the set of positive ...