Question

Let $a_n = 1111111.....1$, where $1$ occurs $n$ number of times. Then, i. $a_{741}$ is not a prime. ii. $a_{534}$ is not a prime. iii. $a_{123}$ is not a prime. iv. $a_{77}$ is not a prime.

Accepted Answer

D. For $a_n$, if $n$ is composite, $a_n$ is composite. $741, 534, 123$ have sum of digits divisible by 3, so $a_n$ is divisible by 3 or $a_3$. $a_{77}$ is divisible by $a_7$ and $a_{11}$. Thus all four are not prime.

Number Theory: Repunit Numbers Prime Check

Explanation

Practise this under exam conditions