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Question

It is given that the number 43361 can be written as a product of two distinct prime numbers p1,p2. Further, assume that there are 42900 numbers which are less than 43361 and are co-prime to it. Then, p1+p2 is

A
462
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B
464
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C
400
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D
402
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Solution

The correct option is D 462
Let's take n=43361 and given that n=p1.p2 where p1, p2 are two prime numbers.
and also given that there are 42900 numbers which are less than 43361 and are co-prime to it. Therefore from Euler's totient function ϕ which states as number of numbers which are less than n and co-prime to it and it is given by ϕ(n)=n1 if n is prime else ϕ(n)=ϕ(p1).ϕ(p2) if n is written as product of those two numbers.
Now, ϕ(43361)=42900=(p11)(p21) 42900=43361(p1+p2)+1 p1+p2=462

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