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Omni-MATH / For a positive integer M, if there exist integers a, b, c and d so that: M≤a<b≤c<d≤M+49, ad=bc then we call M a GOOD number, if not then M is BAD. Please find the greatest GOOD num…

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problem

For a positive integer MM, if there exist integers aa, bb, cc and dd so that: M≤a<b≤c<d≤M+49,ad=bc M \leq a < b \leq c < d \leq M+49, \qquad ad=bc then we call MM a GOOD number, if not then MM is BAD. Please find the greatest GOOD number and the smallest BAD number.
Plain-text mathematical notation (without MathML)
For a positive integer M, if there exist integers a, b, c and d so that:
M≤a<b≤c<d≤M+49, ad=bc
then we call M a GOOD number, if not then M is BAD. Please find the greatest GOOD number and the smallest BAD number.
Original LaTeX notation
For a positive integer $M$, if there exist integers $a$, $b$, $c$ and $d$ so that:
\[ M \leq a < b \leq c < d \leq M+49, \qquad ad=bc \]
then we call $M$ a GOOD number, if not then $M$ is BAD. Please find the greatest GOOD number and the smallest BAD number.

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Source and history

task_id
96b8c3bf-80d8-52d4-b831-f1da9c302046
task_key
test--96b8c3bf-80d8-52d4-b831-f1da9c302046
task_revision_id
5
config / split
/ test

Official source

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