Question

It is given that $43361$ can written as a product of two distinct prime numbers $p_1,p_2$. Further, assume that there are $42900$ numbers which are less than $43361$ and are co-prime to it. Then, $p_1+p_2$ is

• A. 462
• B. 464
• C. 400
• D. 402

Answer 1

The correct option is A 462

Suppose $43361=n$
$n=p_1{p}_2$
$\varphi \left(n\right)=n(1-\frac{1}{p_1})(1-\frac{1}{p_2})=42900$
where $\varphi$ is Euler's totient function.
$\therefore \varphi \left(n\right)=(p_1-1)(p_2-1)\Rightarrow 42900=p_1{p}_2-(p_1+p_2)+1\Rightarrow 42900=43361-(p_1+p_2)+1\Rightarrow (p_1+p_2)=43362-42900=462$