Find 2 consecutive odd integers whose product is -1?

Short answer 1 and - 1.
Algebra
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(k + 2)*k = - 1
k^2 + 2k = - 1
k^2 + 2k + 1 = 0
(k + 1)^2 = 0
k + 1 = 0
k = - 1

Therefore the other odd number is k + 2 = -1 + 2 = 1

-1 and 1

-1 and +1