Question 46
We consider the sets $M = \{0, 1, 2, \dots, 2019\}$ and
$$
A = \left\{ x \in M \mid \frac{x^3 - x}{24} \in \mathbb{N} \right\} .
$$
a)
How many elements has the set $A$?
b)
Determine the smallest positive integer $n$, $n \ge 2$, which has the property that any subset with $n$ elements of the set $A$ contains two distinct elements whose difference is divisible by $40$.
$$
A = \left\{ x \in M \mid \frac{x^3 - x}{24} \in \mathbb{N} \right\} .
$$
a)
How many elements has the set $A$?
b)
Determine the smallest positive integer $n$, $n \ge 2$, which has the property that any subset with $n$ elements of the set $A$ contains two distinct elements whose difference is divisible by $40$.