{
  "problem_id": "IMO2026-P6",
  "day": 2,
  "number": 6,
  "language": "en",
  "statement_markdown": "Let $a_1,a_2,a_3,\\ldots$ be an infinite sequence of positive integers greater than $1$. Suppose that for all positive integers $n$, the number $a_{n+1}$ is the smallest positive integer greater than $a_n$ such that $\\gcd(a_{n+1},a_i)>1$ for every $i=1,2,\\ldots,n$. Prove that there exist positive integers $T$ and $L$ such that\n$$a_{n+T}=a_n+L$$\nfor every positive integer $n$.\n\n(Note that $\\gcd(x,y)$ denotes the greatest common divisor of positive integers $x$ and $y$.)",
  "normalization_changes": [
    "Rendering-only: MathJax SVG glyphs transcribed to LaTeX ($...$ / $$...$$). No semantic change.",
    "Whitespace collapsed; problem parts kept as in source (e.g. (a)/(b), bulleted steps)."
  ],
  "semantic_content_unchanged": true
}