Question 1
Let $n,m$ be natural numbers, with $n\gt 1$. Find the least positive integer $k$ with the following property: among any $k$ integers $a_1,a_2,\ldots,a_k$ such that $a_i-a_j$ is not divisible by $n$ whenever $i\ne j$, there are two terms $a_p,a_s$, $p\ne s$, such that $m+a_p-a_s$ is divisible by $n$.
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.
Dates 19–20 May 1992 are printed; the split into questions 1–3 and 4–6 is editorial because the source has no explicit day divider. All essay rubrics are editorial, and assessment is manual. Importer multipliers are correct 1, incorrect 0, blank 0.
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.
Dates 19–20 May 1992 are printed; the split into questions 1–3 and 4–6 is editorial because the source has no explicit day divider. All essay rubrics are editorial, and assessment is manual. Importer multipliers are correct 1, incorrect 0, blank 0.