Question: How many of the 200 smallest positive integers are congruent to 3 (mod 5)?

Sun, 03 May 2026 03:07:30 +0000

**How Many of the 200 Smallest Positive Integers Are Congruent to 3 (Mod 5)?**
*Answer with clarity, curiosity, and cultural relevance* Ever wondered how numbers line up within modular systems—and why a simple question like “How many of the 200 smallest positive integers are congruent to 3 (mod 5)?” matters in today’s digital landscape? This query may seem technical, but it reflects growing interest in patterns, limits, and number theory—especially among curious minds exploring math, programming, or data structures. In the US, where problem-solving and data literacy shape education and tech culture, questions like this reflect a natural curiosity about order in numbers. **Why This Question Is Gaining Attention**
Interest in modular arithmetic is rising, fueled by trends in coding, algorithm design, and data analysis. Developers and learners often explore how integer sequences behave under modular constraints—such as identifying values congruent to 3 mod 5 within a fixed range. While the number is solution-focused, the question reveals deeper engagement with structured data patterns, especially in fields tied to system efficiency and border-based logic. **How It All Works: A Clear Explanation**
To determine how many of the first 200 positive integers satisfy the condition “congruent to 3 (mod 5),” we apply modular math logic. An integer *n* is congruent to 3 mod 5 if dividing *n* by 5 leaves a remainder of 3—written mathematically as:
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