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Omni-MATH / Consider all ordered pairs of integers (a,b) such that 1≤a≤b≤100 and ((a+b)(a+b+1))/(ab) is an integer. Among these pairs, find the one with largest value of b. If multiple pairs h…

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problem

Consider all ordered pairs of integers (a,b)(a, b) such that 1≤a≤b≤1001 \leq a \leq b \leq 100 and (a+b)(a+b+1)ab\frac{(a+b)(a+b+1)}{a b} is an integer. Among these pairs, find the one with largest value of bb. If multiple pairs have this maximal value of bb, choose the one with largest aa. For example choose (3,85)(3,85) over (2,85)(2,85) over (4,84)(4,84). Note that your answer should be an ordered pair.
Plain-text mathematical notation (without MathML)
Consider all ordered pairs of integers (a,b) such that 1≤a≤b≤100 and ((a+b)(a+b+1))/(ab) is an integer. Among these pairs, find the one with largest value of b. If multiple pairs have this maximal value of b, choose the one with largest a. For example choose (3,85) over (2,85) over (4,84). Note that your answer should be an ordered pair.
Original LaTeX notation
Consider all ordered pairs of integers $(a, b)$ such that $1 \leq a \leq b \leq 100$ and $$\frac{(a+b)(a+b+1)}{a b}$$ is an integer. Among these pairs, find the one with largest value of $b$. If multiple pairs have this maximal value of $b$, choose the one with largest $a$. For example choose $(3,85)$ over $(2,85)$ over $(4,84)$. Note that your answer should be an ordered pair.

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Source and history

task_id
3053b5df-db43-5d56-a6ae-89eafa3f3a25
task_key
test--3053b5df-db43-5d56-a6ae-89eafa3f3a25
task_revision_id
1
config / split
/ test

Official source

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