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2020 USOJMO Problems/Problem 5: Difference between revisions

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Created page with "Suppose that <math>(a_1,b_1),</math> <math>(a_2,b_2),</math> <math>\dots,</math> <math>(a_{100},b_{100})</math> are distinct ordered pairs of nonnegative integers. Let <math>N..."
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Revision as of 09:13, 24 June 2020

Suppose that $(a_1,b_1),$ $(a_2,b_2),$ $\dots,$ $(a_{100},b_{100})$ are distinct ordered pairs of nonnegative integers. Let $N$ denote the number of pairs of integers $(i,j)$ satisfying $1\leq i<j\leq 100$ and $|a_ib_j-a_jb_i|=1$. Determine the largest possible value of $N$ over all possible choices of the $100$ ordered pairs.

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