Understanding Integer Properties and Differences of Squares

The video tutorial explores a mathematical problem involving two integers, p and n, where p is greater than n and both are positive. The equation p^2 - n^2 = 12 is given, and the task is to determine possible values for p-n. The solution involves factoring the equation as a difference of squares, leading to the expression (p+n)(p-n) = 12. Various combinations of positive integers that multiply to 12 are considered, and scenarios are evaluated to find integer solutions. The conclusion is that the only possible value for p-n is 2.

What is the relationship between p and n in the given problem?

• p is greater than n

• p and n are not related

• p is equal to n

• p is less than n

What equation is given in the problem involving p and n?

• p^2 + n^2 = 12

• p + n = 12

• p^2 - n^2 = 12

• p - n = 12

How can the expression p^2 - n^2 be factored?

• (p - n)(p - n)

• (p + n)(p - n)

• (p + n)(p + n)

• (p^2 - n^2)

What are the possible integer combinations for p + n and p - n that multiply to 12?

• 8 and 4, 6 and 3, 5 and 2

• 7 and 5, 6 and 1, 4 and 2

• 10 and 2, 5 and 2, 3 and 4

• 12 and 1, 6 and 2, 4 and 3

Why is the scenario where p + n = 12 and p - n = 1 not possible?

• n becomes a non-integer

• n becomes a negative integer

• p becomes a non-integer

• p becomes a negative integer

In the scenario where p + n = 6 and p - n = 2, what is the value of p?

• 2

• 3

• 4

• 5

What is the value of n in the scenario where p + n = 6 and p - n = 2?

• 3

• 4

• 2

• 1

Why is the scenario where p + n = 4 and p - n = 3 not possible?

• p becomes a non-integer

• n becomes a non-integer

• n becomes a negative integer

• p becomes a negative integer

What is the only possible value of p - n?

• 4

• 3

• 2

• 1

Which of the following is true about the integers p and n?

• p and n are equal

• p is less than n

• p is greater than n

• p and n are negative