64
Let $p, q$ and $r$ be three distinct prime numbers. Check whether $p \cdot q \cdot r + q$ is a composite number or not. Further, give an example for 3 distinct primes $p, q, r$ such that (i) $p \cdot q \cdot r + 1$ is a composite number. (ii) $p \cdot q \cdot r + 1$ is a prime number.
Show SolutionHide Solution↓
$p \cdot q \cdot r + q = q(pr + 1)$. Thus, the given number has more than 2 factors. Hence it is composite ($\frac{1}{2} + \frac{1}{2}$ marks). (i) Taking $p=3, q=5$ and $r=7$, $pqr + 1 = 3 \cdot 5 \cdot 7 + 1 = 106$ is a composite number (1 mark). (ii) Taking $p=2, q=3$ and $r=5$, $pqr + 1 = 2 \cdot 3 \cdot 5 + 1 = 31$ is a prime number (1 mark).