Solution:
Let x be the first integer.
Then x+1 is the next integer.
The product is 506
x(x+1) = 506
x2 + x = 506
x2 + x - 506 = 0
\( x_1 = \frac{-1+\sqrt{1+4(1)(506)}}{2(1)} = 22\)
Answer: 22 and 23