Number Theory: Repunit Numbers Prime Check

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.

Answer

(i) is correct.

Answer

(i) and (ii) are correct.

Answer

(ii) and (iii) are correct.

Answer

All of them are correct.

Answer

None of them is correct.

Number Theory: Repunit Numbers Prime Check

Explanation

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