Chapter 5, Problem 7P

(a)

To determine

To calculate: The values of n for which $n^{th}$ row divisible by n in Pascal’s Triangle if $1\le n\le 12$ and it is given that $7^{th}$ row of Pascal’s Triangle is divisible by 7.

(b)

To determine

The each interior values of $n^{th}$ row of Pascal’s Triangle is divisible by n if $n=1,2,3,5,7\text{ and }11$, and it is given that $7^{th}$ row of Pascal’s Triangle is divisible by 7. The Pascal’s Triangle for ${12}^{th}$ row,

(c)

To determine

The sum of interior number of $P^{th}$ row is $2^P-2$ for any prime number P.

(d)

To determine

To calculate: The value of $2^P-2$ for $P=7$ and $2^P-2$ is a multiple of 7.

(e)

To determine

The $2^P-2$ is multiple of P if P is any prime number. It is given that for any prime number P the sum of interior number of $P^{th}$ row is $2^P-2$ and the each interior values of $P^{th}$ row of Pascal’s Triangle is divisible by P if $P=1,2,3,5,7\text{ and }11$.

The Pascal’s Triangle for ${12}^{th}$ row,