Question

define Q(q): for all value of p in N, where p<q such that NOT(there exist k in N, where (q=k*p)^(k<q))
Concisely, for which numbers q in N, when Q(q) is true?

Answer 1

Answer on Question #63196 – Math – Discrete Mathematics

Question

Define $Q(q)$: for all values of $p \in \mathbb{N}$, where $p < q$ such that NOT (there exists $k \in \mathbb{N}$, where

$$(q = k * p) \wedge (k < q)).$$

Concisely, for which numbers $q \in \mathbb{N}$, when $Q(q)$ is true?

Solution

Let $\mathbb{N}$ be a set of numbers. Obviously, the statement $Q(q)$ is true for number $q \in \mathbb{N}$ iff the subset of its proper factors, i.e. all factors strictly less than itself, is empty or consists of one element.

Let $\mathbb{N}$ denote the set of natural numbers. The statement $Q(q)$ is true iff $q$ is a prime number or 1.

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