Replay available 5/28/2021 Go to Http://lims.flaels.org to register.Florida Hemp
Hello,
This is a reminder to join the Florida Department of Agriculture and Consumer Services for a town hall meeting with the Cannabis Director on May 27th, from 3:00 – 4:00 p.m.
Please see the attached agenda for more information.
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 offigurate numbers: thesquare triangular numbers, which are simultaneously square and triangular, and the solutions to thecannonball 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 theMordell curves, which areelliptic curvesof the form
y2=x3+k.
When
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 byRudolf FueterandLouis J. Mordell, states that, when
k
is an integer that is not divisible by a sixth power (other than the exceptional cases
k=1
and
k=−432
), this equation either has no rational solutions with both
x
and
y
nonzero or infinitely many of them.
In thearchaic notationofRobert 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 centuryIndian mathematicsbyBhāskara IIalso called them either the square of a cube or the cube of a square.
