The difference between the squares of two consecutive integers is 31. What is the smaller integer?
["The difference between the squares of two consecutive integers is 31. What is the smaller integer? \nIt’s a straightforward math question many pause over—why does squaring one whole number and skipping ahead to the next produce a difference of 31? This idea has quietly gained traction in digital spaces, especially among curious learners and students exploring patterns in numbers. Understanding this concept reveals a hidden logic behind seemingly simple arithmetic.", "Why this question is gaining attention in the US \nIn a world where math is increasingly tied to logic puzzles and cognitive engagement, this question reflects growing interest in problem-solving fundamentals. Users are drawn to snippets that unlock patterns—not just the answer, but the reasoning behind it. With more people revisiting early math topics for personal growth, mental agility, or academic reinforcement, the focus on "squares of consecutive integers" offers a relatable bridge between basic arithmetic and deeper mathematical thinking.", "The idea that “the difference between the squares of two consecutive integers is 31” fits naturally into this trend. It invites exploration without overt complexity—ideal for users searching for clear, self-guided learning moments on mobile devices.", "How the difference between the squares of two consecutive integers works \nFor two consecutive integers, let the smaller be n. Then the next integer is n + 1. Their squares are n² and (n + 1)². \nThe difference is: \n*(n + 1)² – n²* \nExpanding gives: n² + 2n + 1 – n² \nWhich simplifies to: 2n + 1 \nSetting this equal to 31: \n2n + 1 = 31 \nSubtracting 1 from both sides: \n2n = 30 \nDividing by 2: \nn = 15", "The smaller integer is therefore 15. This formula—2n + 1—now serves as a quick rule for anyone curious about"]
