Let x be the first odd integer and x + 2 be the second intger.
\(x(x+2) = 1023\)
\(x^2 +2x = 1023\)
\(x^2 +2x -1023 =0 \)
\((x+33)(x-31) =0 \)
\(x_1 =-33 \)
\(x_2 =31 \)
The first integer is 31 and the second integer is 33.