The number of integers \(n\) such that \(1 \leq n \leq 10^7\) and \(\gcd(n, 10^7) = 10^3\) is ___
Question and options
The number of integers such that and is ___
- 3000
- 2000
- 5000
- 4000
Answer and explanation
Correct answer: D - 4000
n = 1000m with 1 <= m <= 10^4 and gcd(m, 10^4) = 1 (m coprime to 10). Count = phi(10^4) = 10^4 * (1/2)(4/5) = 4000.
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