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Question

It is given that 43361 can 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 A 462
Suppose 43361=n
n=p1p2
ϕ(n)=n(11p1)(11p2)=42900
where ϕ is Euler's totient function.
ϕ(n)=(p11)(p21)42900=p1p2(p1+p2)+142900=43361(p1+p2)+1(p1+p2)=4336242900=462

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