MathDB
Good and bad

Source: China TST 2006

June 18, 2006
number theory unsolvednumber theory

Problem Statement

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.
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