Find the largest 'good' number

Algebra Level 3

A number M M will be called good if there exists a , b , c , d a,b,c,d such that M a < b c < d M + 49 M\le a<b\le c<d\le M+49 and a d = b c . ad=bc.

What is the largest good number?


The answer is 576.

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