A number theory problem by Saswata Naha

Number Theory Level 3

It is given that

  1. n = 46118929 n=46118929 is the product of two primes p p and q q .
  2. The number of positive integers less than n n and relatively prime to n n is 46093860.

Find the value of p + q p+q .

25070 25700 46118930 Can not be determined.

Saswata Naha by Saswata Naha , 20, India

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2 solutions

Avik Das
Jan 30, 2019

n=pq then the no.s which are not relatively prime with n and less than or equal to n are of the form p, 2p, 3p, 4p,...,(q-1)p and q, 2q, 3q,...,(p-1)q and pq so, total no. of co primes with n and less than n is 46118929-(p-1)-(q-1)-1= 46093860 or, p+q=46118929-46093860+1+1-1=25070

1 Helpful 1 Interesting 1 Brilliant 1 Confused
Saswata Naha
Apr 21, 2017

1 Helpful 0 Interesting 0 Brilliant 1 Confused

You still have to prove the existence of 2 primes that satisfy these conditions.

Pi Han Goh - 4 years, 1 month ago

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