Your Math Buddy

Algebra | Factoring Polynomials (Special Products)

Don't forget to follow and share my page: www.facebook.com/mathcornerph/

and subscribe to my YouTube Channel:
https://www.youtube.com/channel/UCEwVK93iQbUx5Tsx2mwNFYg

Let's grow together 🤝

😮

The 65-year-old problem, x³+y³+z³=42, has finally been solved!

A team led by Professor Andrew Booker from the University of Brisol, who also groundbreakingly found a solution to three cubes whose sum is 33, and Professor Andrew Sutherlands from Massachusetts Institute of Technology (MIT) used the Charity Engine, a worldwide supercomputer program and tapped almost 400,000 home PC's to solve the integers that would satisfy the Diophantine Equation:

x³+y³+z³=42

The solution to this Diophantine equation is
x=-80538738812075974
y=80435758145817515
z=12602123297335631

Originally, the 65-year old problem came from the University of Cambridge where they looked for the solutions of a Diophantine Equation x³+y³+z³=k where k is a positive integer between 1 and 100 and x, y, and z are integers. Initially, some numbers have small solutions and mathematicians and programmers need not to make any programs to solve the problems. For instance, if k=3, then x=y=z=1. It has never been easy until the case for k=33 and k=42 became the most difficult and unsolvable.

Note that there are some integers between 0 to 100 that will not have solutions, or it cannot be written as a sum of three cubes. These are numbers that are in the form 9k+4 and 9k+5 where k is an integer (this can be proved using concepts from number theory). Thus, 4,5,13,14,22,23,31, and 32 cannot be written as a sum of 3 cubes.

There are so many questions in mathematics that are left unanswered up to this date. It is thanks to mathematicians today that we get to learn more about how specific objects interact and patterns involving such objects. Thanks to the knowledge contributed by mathematicians, we will be a step closer towards understanding more about life and the universe itself.

References:
Booker, A. (2019). Cracking the problem with 33. Research in Number Theory, [online] 5(3). Available at: [Accessed 8 September 2020].
Miller, S. (2019). Sutherland Helps Solve Decades-Old Sum-Of-Three-Cubes Puzzle. [online] MIT School of Science. Available at: [Accessed 8 September 2020].
Miller, S. (2019). The Answer To Life, The Universe, And Everything. [online] MIT News | Massachusetts Institute of Technology. Available at: [Accessed 8 September 2020].
Phys.org. (2019). Sum Of Three Cubes For 42 Finally Solved—Using Real Life Planetary Computer. [online] Available at: [Accessed 8 September 2020].

Differential Calculus (Basic Calculus) - Power, Product and Quotient Rule https://youtu.be/KgPt0l2Zt8c

Don't forget to subscribe to my YouTube Channel : https://www.youtube.com/channel/UCEwVK93iQbUx5Tsx2mwNFYg

Differential Calculus | Power, Product and Quotient Rule This topic is about derivative which is commonly taken in Basic Calculus (SHS) and Differential Calculus (College) P.S. Hindi ko na naedit yung part ng "Topi...

Algebra | Laws of Logarithms

Don't forget to follow and share my page: www.facebook.com/mathcornerph/

and subscribe to my YouTube Channel:
https://www.youtube.com/channel/UCEwVK93iQbUx5Tsx2mwNFYg

Let's grow together 🤝

Pre-Calculus | Conic Sections (Circle - Part 1)

Make sure to subscribe to my YouTube Channel to keep you updated. Thank you 😊

Conic Sections | Circle (Part 1) This is a topic in Pre-Calculus. Conic sections involves Circle, Parabola, Ellipse and Hyperbola.

General Mathematics | Logic

Please don't forget to like and share my page: https://www.facebook.com/mathcornerph/

Also, please subscribe to my YouTube Channel : https://www.youtube.com/channel/UCEwVK93iQbUx5Tsx2mwNFYg

Let's grow together 🤝😊
Thank you 😊

Trigonometry | Formulas and Identities

Don't forget to follow and like my page :
https://www.facebook.com/mathcornerph/

And subscribe to my YouTube Channel : https://www.youtube.com/channel/UCEwVK93iQbUx5Tsx2mwNFYg

Thank you 😊

Differential Equation | Random Math Problem

Let's grow together 🤝

Don't forget to like and share my page (https://www.facebook.com/mathcornerph/) for more math contents. 😊

Feel free to suggest any math topics 😊

Pre-Calculus | Conic Sections

Don't forget to subscribe to my YouTube Channel for more detailed explanations.
https://www.youtube.com/channel/UCEwVK93iQbUx5Tsx2mwNFYg

Here is my first lecture video 😊
Algebra | Laws of Exponents

Don't forget to subscribe! 😉
Feel free to suggest any math topics.
Thank you 😊

Algebra | Laws of Exponents This is a topic in Algebra which is about Laws of Exponents.