Hi, 

find three  positive integers

 What is the smallest integer? 

 What is the second smallest integer? (n+1)

 What is the largest integer? (n+2)

product of the first and third, minus the second, is 1 more than 6 times the third.

 n(n+2) - (n+1) = 6(n+2)+1

 n^2 -5n -14 = 0

(n+2)(n-7) = 0,  (tossing out the negative solution for n)

the three consecutive positive integers are: 7,8,9

CHECKING our Answer***

 7*9 - 8 = 55 = 6*9 + 1

   

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