Prime *prime
Number Theory
Level
pending
- You are told that n = 110179 is the product of two primes p and q. The number of positive integers less than n that are relatively prime to n (i.e. those m such that gcd(m, n) = 1) is 109480. Write the value of p + q.
The answer is 700.
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1 solution
n = p q
Number of numbers less than or equal to n that are multiple of p = q .
Number of numbers less than or equal to n that are multiple of q = p .
Number of numbers less than or equal to n that are multiple of p q = 1
Number of numbers less than or equal to n that are co-prime to n = p q − p − q + 1
p + q = 1 1 0 1 7 9 − 1 0 9 4 8 0 + 1 = 7 0 0