Question 164036
Let:
the first odd integer = x
the second odd integer = x + 2
the third odd integer = x + 4

{{{x*(x + 4) = (x + 2)^2 - 4}}}
<=> {{{x^2 + 4x = x^2 + 4x + 4 - 4}}}
<=> {{{x^2 + 4x - x^2 - 4x = 4 - 4}}}
<=> {{{0 = 0}}}

from the result above, we can conclude that every 3 consecutive odd integers has such characteristic (the product of the first and third integers is 4 less than the square of the second integer)
{{{1*5 = 3^2 - 4}}}
{{{3*7 = 5^2 - 4}}}
{{{5*9 = 7^2 - 4}}}
and so on.