An ichthyologist is studying coral reef fish populations and models their seasonal counts. What two-digit positive integer is one more than a multiple of 3, one more than a multiple of 4, and also one more than a multiple of 5?

What two-digit positive integer is one more than a multiple of 3, 4, and 5?
An ichthyologist is studying coral reef fish populations and models their seasonal counts. What two-digit positive integer is one more than a multiple of 3, one more than a multiple of 4, and also one more than a multiple of 5?

Right now, a quiet but growing conversation is unfolding in scientific and environmental circles: how tracking fish populations can reveal deeper truths about reef health, climate change, and biodiversity. Curious about how these patterns emerge—and why a simple number connects to them? The answer lies in modular arithmetic, a tool that reveals hidden order beneath natural rhythms.

Why This Number Matters in Science and Data

Understanding the Context

People are increasingly interested in seasonal trends across ecosystems. An ichthyologist models coral reef fish populations by analyzing monthly counts, revealing seasonal peaks, population cycles, and responses to environmental shifts. This kind of data modeling helps scientists predict resilience, assess conservation needs, and understand how marine life adapts over time.

The number described—one more than a multiple of 3, 4, and 5—represents a rare alignment in modular arithmetic. It satisfies a condition known in number theory: finding integers n such that n ≡ 1 mod 3, n ≡ 1 mod 4, and n ≡ 1 mod 5. Solving this system reveals a consistent pattern—useful not just for math, but for tracking recurring natural events like fish spawning or migration patterns.

How This Number Actually Works

To find the two-digit integer satisfying all three conditions, start by noting that if a number is one more than a multiple of 3, 4, and 5, it’s equivalent to finding n such that:
n = LCM(3,4,5) × k + 1