17 and 19 are odd, consecutive integers whose product is 323.
Algebraic explanation:
Let x be the first unknown. Then x+2 must be the second unknown.
x*(x+2)= 323" " Set up equation
x^2+2x = 323" " Distribute
x^2+2x-323 = 0 " " Set equal to zero
(x-17)(x-19)=0 " " Zero product property
x-17 = 0 or x-19=0" " Solve each equation
x= 17 or x= 19