All Questions
49
questions
5
votes
4
answers
621
views
${{p-1}\choose{j}}\equiv(-1)^j \pmod p$ for prime $p$
Can anyone share a link to proof of this?
$${{p-1}\choose{j}}\equiv(-1)^j(\text{mod}\ p)$$ for prime $p$.
- 4,793
3
votes
2
answers
166
views
Counting the number of matrices which cause collision
Let $m,n \in \mathbb{N}$, and $q$ be a prime number.
Let $\mathbf{A} \in \mathbb{Z}^{m \times n}_q$ be a matrix. In the following, assume that all additions and multiplications are performed modulo $...
- 3,331
2
votes
0
answers
848
views
$a^{(b^c)} \mod m$ where $c$ can be very very large
I am trying to solve the following problem.
I need to find the value of
$$
a^{(b^x)} \bmod m
$$
where $a,b$ are integers and
$$
x = \pmatrix{n\\0}^2 + \pmatrix{n\\1}^2 + ... + \pmatrix{n\\n}^2 ...
- 33
1
vote
2
answers
517
views
Solutions to $x_1+2x_2+3x_3+4x_4+5x_5+6x_6+7x_7+8x_8+9x_9+10x_{10}\equiv0\mod11$
How many solutions does the following equation have:
$x_1+2x_2+3x_3+4x_4+5x_5+6x_6+7x_7+8x_8+9x_9+10x_{10}\equiv0\mod11$
where
$x_{1...9} \in \{0,1,2,3,4\ ...\ 8,9\}$ and $x_{10}\in\{0,1,2,3,4\ ...\...
- 179