Question: How many of the 100 smallest positive integers represent positions in a DNA sequence that are congruent to 3 mod 5?

Sun, 03 May 2026 15:05:42 +0000

**How Many of the 100 Smallest Positive Integers Are Congruent to 3 Mod 5?**
*And What It Reveals About Patterns in DNA* Curious readers are increasingly exploring how mathematical concepts shape real-world science—especially genetics. One intriguing query gaining attention among biology and data enthusiasts is: *How many of the 100 smallest positive integers correspond to positions in a DNA sequence that are congruent to 3 mod 5?* This question isn’t just academic—it reflects growing interest in decoding genetic patterns using modular arithmetic. Mathematically, a number is “congruent to 3 mod 5” when dividing by 5 leaves a remainder of 3. The first few such positive integers are 3, 8, 13, 18, 23, 28, 33, 38, 43, and 48—exactly 10 values within the first 100 positive integers. Why is this topic resonating now? In the U.S., public engagement with genomics has surged alongside advances in personalized medicine, direct-to-consumer DNA testing, and research into inherited health patterns. When users ask how modular positions structure DNA, it signals a tasteful curiosity about underlying biological codes—driven by curiosity, not explicit content.