Math News: Prime Numbers 5

1- The final number of terms of a polynomial of 4 terms is found by adding the
numbers in a row of Jaramillo’s triangle.
2- The triangle is symmetrical.
3- The product of the partial results is a perfect square and if the perfect square
is divided by the one before, the result is also a perfect square.
4- The central column of the triangle is made up of perfect squares.
5- Since the triangle is symmetrical, the ”centered” numbers multiplied together
are equal to the product of ALL the numbers of the row before.

Example:
3x4x4
4x6x6x4 -> 6x6 = 3x4x3
Just as 8x9x8 = 4x6x6x4

6- The square root of the product of the partial results is equal to the first number
of the row factorial.

3x4x6=36 and 361/2=6=3!
4x6x6x4=576 and 5761/2=24=4!

Many experiments can be conducted by dropping the diagonals so that a new triangle is obtained:
4
6 6
8 9 8
10 12 12 10
12 15 16 14 12 and so on.

This triangle is also symmetrical and the product of the entries in the rows is also a perfect square. It is interesting to see that the square root of the perfect square obtained is equal to
the number dropped minus one factorial:

41/2=2=(3-1)!