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(1−1p1)(1−1p2)=42900 where ϕ is Euler's totient function. ∴ϕ(n)=(p1−1)(p2−1)⇒42900=p1p2−(p1+p2)+1⇒42900=43361−(p1+p2)+1⇒(p1+p2)=43362−42900=462