GATE | GATE CS 2019 | Question 60

In an RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also is known that φ(n) = 2880, where φ( ) denotes Euler’s Totient Function, then the prime factors of n which is greater than 50 is _________ .

Note: This was Numerical Type question.
(A) 97
(B) 31
(C) 37
(D) 91


Answer: (A)

Explanation: Given,

n = p * q = 3007  ... ... (1) 

And,

φ(n) = (p - 1) * (q - 1) = 2880 ... ... (2) 

→ pq - p - q + 1 = 2880
→ 3007 - p - q + 1 = 2880
→ p + q = 128 ......(2) 

Using equation (1) and (2),

→ (3007 / q) + q = 128

→ q2 - (128*q) + 3007 = 0 

On solving the above equation:

q = 31, 97  

97 is greater than 50.

So, option (A) is correct.


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