#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#