Month: May 2021

Please Consider My Wish!

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Eight Squared

 1 2 4 9 16 25 36 49 64

Sixty Four Squares

2x2x2x2x2x2 or

2 to the 6th Power = 64

From Wikipedia

The sixth powers of integers can be characterized as the numbers that are simultaneously squares and cubes. In this way, they are related to two other classes of figurate numbers: the square triangular numbers, which are simultaneously square and triangular, and the solutions to the cannonball problem, which are simultaneously square and square-pyramidal.

Because of their connection to squares and cubes, sixth powers play an important role in the study of the Mordell curves, which are elliptic curves of the form

${\displaystyle y^2=x^3+k.}$

When 

${\displaystyle k}$

 is divisible by a sixth power, this equation can be reduced by dividing by that power to give a simpler equation of the same form. A well-known result in number theory, proven by Rudolf Fueter and Louis J. Mordell, states that, when 

${\displaystyle k}$

 is an integer that is not divisible by a sixth power (other than the exceptional cases 

${\displaystyle k=1}$

 and 

${\displaystyle k=-432}$

), this equation either has no rational solutions with both 

${\displaystyle x}$

and 

${\displaystyle y}$

 nonzero or infinitely many of them.

In the archaic notation of Robert Recorde, the sixth power of a number was called the “zenzicube”, meaning the square of a cube. Similarly, the notation for sixth powers used in 12th century Indian mathematics by Bhāskara II also called them either the square of a cube or the cube of a square.

*****May21*********************2021******************** *********************

81 will be my next square in my life of numbers.

Steven Michael Smith

Happy 64th Birthday, Steve. InspirationalTech.Org

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