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Please solve this question 
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Asked by vikasg13.hardware | 30 Jun, 2018, 06:57: AM
answered-by-expert Expert Answer
33pq - n = 0 (mod 3)
33pq - n = 0 (mod p)
33pq - n = 0 (mod q)
We need to satisfy following conditions
i (3 - 1)| (pq - 1) hence, pq is odd
ii (p - 1) | (3q - 1) 
3 must not divide p - 1 as it does not divide 3q - 1
p - 1 = 3m + 1 or 3m + 2 for some integer m
Hence, p = 3m + 2 or 3m + 3
But p ≠ 3m + 3 as it is prime
Hence, p = 3m + 2
p > 3 and m = odd = 2k + 1 
p = 6k + 5
(q - 1) | (3p - 1) so q will also be 5 (mod 6)
Using trial least value of p and q are 17 and 11
Hence, p + q = 28
 
 
 
 
Answered by Sneha shidid | 02 Jul, 2018, 10:07: AM

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