**Quote:**

What does the # symbol mean in these types of questions?

Such symbols as #, @, etc., which are not used in the school math, define a new mathematical operation.

In school we learn basic mathematical operations, such as

*addition *(+),

*subtraction *(–),

*multiplication *(×), etc.

Similarly, the # sign defines a new mathematical operation. a#b

**IS** (a – b)(a + b).

4#3 = (4 – 3)(4 + 3) = 7

1#2 = (1 – 2)(1 + 2) = -3

....