Question: Find the smallest positive integer whose square ends in 625.

Fri, 01 May 2026 22:21:01 +0000

**Why More People Are Exploring the Integer Ending in 625**
The digital curiosity around number patterns has resurged, with users across the United States increasingly drawn to mathematical puzzles that reveal hidden logic in everyday life. One such intriguing question is: *Find the smallest positive integer whose square ends in 625.* Though seemingly niche, this query reflects a broader interest in pattern recognition, number theory, and practical math applications—especially among mobile users seeking smart, reliable facts in a mobile-first world. As digital learning and self-education grow, this question surfaces frequently in search behavior, signaling a desire to connect abstract math with tangible outcomes. **Why This Question Is Crossing into Mainstream Awareness**
Across the U.S., from classrooms to informal learning spaces, people are exploring how numbers behave in predictable—and surprising—ways. The square ending in 625 isn’t just a textbook example; it’s a real-world puzzle users encounter in coding, data modeling, and even cryptography basics. Social cues like viral problem-solving threads on platforms popular with U.S. audiences amplify interest, turning a simple math question into a shared intellectual challenge. The overlap of number curiosity with digital habit formation fuels ongoing engagement, making it a strong candidate for top Discover placement. **How the Integer Ending in 625 Actually Works**
To solve *Find the smallest positive integer whose square ends in 625*, we rely on modular mathematics, specifically looking at how numbers behave modulo 1000. A square ending in 625 means:
*n² ≡ 625 (mod 1000)*
We know 625 = 25², so the last three digits of a perfect square in this form trace to numbers ending in or related to 25. Testing small integers reveals that 125 is the smallest such value:
125² = 15,625, which ends in 625. Smaller candidates like 25 (25² = 625) work, but 25² ends in exactly 625—so it qualifies. However