Category: Updates

Last digits of primes

A prime number not equal to $2$ and $5$ can't have last digit equal to $2,4,5,6$ and $8$. Is it true that this is the only restriction on last digits...

Arranging balls in a row

Let $m$ white balls and $n$ black balls. We arrange them randomly in a row. Let $k_1,\ldots, k_j \in\mathbb{N}$ such that $k_1 + \cdots + k_j = m$. What&#...

$y'=y(y-1)(y-2)$ [duplicate]

Consider the differential equation $$y'=y(y-1)(y-2)$$ Which of the following statements is true ? If $y(0)=0.5$ then y is decreasing. If $y(0)=1.2$ t...