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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…

Problem

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problem

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.

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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task_id: 96b8c3bf-80d8-52d4-b831-f1da9c302046
task_key: test--96b8c3bf-80d8-52d4-b831-f1da9c302046
task_revision_id: 4
config / split: / test

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