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(a) For which values of $n > 2$ is there a set of $n$ consecutive positive integers such that the largest number in the set is a divisor of the least common multiple of the remaining $n - 1$ numbers?

(b) For which values of $n > 2$ is there exactly one set having the stated property?

Initially, two positive integers $a$ and $b$ with $a \neq b$ are written on a blackboard. At each step, Andrea picks two numbers $x$ and $y$ on the blackboard with $x \neq y$ and writes the number

$$\gcd(x, y) + \operatorname{lcm}(x, y)$$

on the blackboard as well. Let $n$ be a positive integer. Prove that, regardless of the values of $a$ and $b$, Andrea can perform a finite number of steps such that a multiple of $n$ appears on the blackboard.

Remark. If $x$ and $y$ are two positive integers, then $\gcd(x, y)$ denotes their greatest common divisor and $\operatorname{lcm}(x, y)$ their least common multiple.

Odredi sve uređene parove $(a,b)$ prirodnih brojeva takve da je $V(a,b) - D(a,b) = \dfrac{ab}{5}$.

Odredi sve prirodne brojeve $a$ i $b$ takve da je $$a^2 = 4b + 3 \cdot V(a, b),$$ pri čemu $V(m,n)$ označava najmanji zajednički višekratnik brojeva $m$ i $n$.