It is given that the number 43361 can be writ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The number of integers less than $n$ and coprime to $n$ is given by Euler's totient function $\phi(n)$.Given $n = p_1 	imes p_2$,where $p_1$ and

Vedclass · Accepted Answer

$462$

Vedclass · Answer

(A) The number of integers less than $n$ and coprime to $n$ is given by Euler's totient function $\phi(n)$.Given $n = p_1 	imes p_2$,where $p_1$ and $p_2$ are distinct primes,the formula for $\phi(n)$ is $\phi(n) = (p_1-1)(p_2-1)$.We are given $\phi(43361) = 42900$.So,$(p_1-1)(p_2-1) = 42900$.Expanding this,$p_1 p_2 - p_1 - p_2 + 1 = 42900$.Since $p_1 p_2 = 43361$,we have $43361 - (p_1+p_2) + 1 = 42900$.$43362 - (p_1+p_2) = 42900$.$p_1+p_2 = 43362 - 42900 = 462$.Thus,the sum of the two prime factors is $462$.

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

Similar Questions

The number of ways of awarding $9$ scholarships among $3$ students so that each may have $3$ scholarships is

What is the highest power of $3$ in $100!$?

The coefficient of $a^{10} b^7 c^3$ in the expansion of $(bc + ca + ab)^{10}$ is

The number of positive divisors of $360$ which are multiples of $3$ is

The largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module