the three consecutive integers can be written as:

x-1, x, x+1, where x is integer

the sum of three consecutive integers is 582

x - 1 + x + x + 1 = 582

by solving we find

x = 194

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194 - 1 = 193

194 + 1 = 195

indeed

193 + 194 + 195 = 582

the three consecutive integers are 193, 194 and 195.