Commander

Yes, 33 + 43 + 53 = 63 Many Solutions for a3 + b3 = c2 might be found I think. like 13 + 23 = 32 , It is also very interesting to note that [13+23+33 ... + n3] = [1+2+3 .....+n]2 = [n (n+1) /2] 2

Hi imatfaal and Michel123456, I am very sorry. After I checked again with the help of the tool it appears my interpretation was wrong. So it is only z = [ 31/2 (3xy3 - x4) 1/2 - 3x2 ] / 6x and therefore we need to contend with Square root of 3 which is an irrational number ! Because this is the Solution for z in the Equation y3 + z3 = (z+x)3 or y3 = (z+x)3 - z3 as a Sum or difference between Cubic Numbers and therefore the solution to y3 + z3 = n3 has only an irrational Value and hence proves the Fermat's Conjecture for the Power of 3.

Hi imatfaal, Yes, Thank you. That's the Equation and the last term 6x on the numerator can be dropped too. Then z will become z -1 and that is OK too as an integer. I am unable to draw it out correctly Regards

I think that the equation indicates (4xy3 - x4)1/3 rather than 31/2 multiplied by(4xy3 - x4)1/2

I have a theory that Everything is Unique in our Universe ! By this I don't mean the Simple Proof that Every Point in our Universe is Uniquely Different from another in factors such as Latitude, Longitude or X,Y,Z Coordinates but in a more tangible way !! We have many Life Forms and Everything is Evolving too. There is a definite Genetic Signature of Each Species and within the same Species the DNA can be used to differentiate within the same Species. Every Person, Personality, Plant or Animal Life is different. Following this Logic it is impossible to produce anything identical to anything else. Exact Replica. Even in the Manufacturing line the Serial Number and Time Stamp of Finishing that Product will be different. From the Practical Point of View I would like to state that even within the Human Body all Cells will not be identical having exactly identical DNA etc [though large similarity can be identified] which explains what causes Mutation and Evolution. I can justifiably extend the same Logic to even to non-animate bodies and say that no Particle , atom, Molecule etc too can never be an exact duplicate of another !!! Though in many cases it does not matter to vary slightly and can be treated to be IDENTICAL !!!!

Hi, Thanks. It is the Cubic Root of the segment under the bar

Good Governance = (Number on InCorruptible Politicians - Number of Corrupt Politicians) + (Number of Honest Judges - Number of Corrupt Judges) + (Number of Liar Lawyers - Number of Honest Lawyers) + (Number of Honest Police Officers & Bureaucrats - Number of Dishonest Police Officers & Bureaucrats) + (Number of Non-Bribing Citizens - Number of Bribing Citizens) + (Number of Honest Journalists - Number of Paid Journalists) - (Number of Disruptionists such as Hate Spreaders, Terrorists of every Hue etc) ! This number is HEAVILY NEGATIVE in any Failed State !! >>>>>>>>>>>>>>>>>>>>>> Ten Commandments >>>>>> [1] Never trust the witness of racist in any race related issues ! [2] Never trust the words of a person in a crowd in support of what that crowd stands for ! [3] Always mark as truth the witness of a poor man if he is free and unencumbered to make that confession ! [4] The person who is less hurt but makes more noise is the culprit ! [5] Any law which prevents truth from emerging is the act of the Devil [6] The nation which does not deliver equal justice is a failed state [7] Never listen to the oratory of a speaker if there is no valid points spoken of [8] Trust the witness of an atheist in the case of inter religious problems [9] A winner who never tasted a loss is less reliable than the loser who managed to win [10] Today's Happy Existence is better than tomorrow's Promise !

If light cannot escape a black hole, then ........ Einstein argues, … the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity") to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies. The introduction of a "luminiferous ether" will prove to be superfluous in as much as the view here to be developed will not require an "absolutely stationary space" provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place. ................ It shows that Einstein did believe in Empty Space which he has quoted, and also thought that Light is not affected by Gravity ! BLACK HOLE ? Therefore, lot has happened since Einstein too !!

Tell me what you know if you can - What is this Global Warming Scare ? Give me the Equations.

Hi Strange, Thanks. Yes, it might be insignificant but I would like to study what are the Parameters taken into the Global warming Phenomenon before taking a final call/opinion !

Still trying hard to find a possible solution to a3 + b3 = c3 If we have any Integer Solution to x, y, z in the above equation then we have a Solution to a3 + b3 = c3 with a,b,c as integers.

Hi Sensei, Thanks. Yes, that is quite a bit of energy received per Sq m of Earth's Surface. That shows how much Energy Sun is losing. Can you quantify that and how much is the mass of Sun getting reduced as a result as per our current understanding. Maybe the larger parts of that will be leaving the Solar System once and for all. Regards

Hi Swansont, Thanks. Yes it is interesting to study everything about the Sun. While Sun's Surface temp is reported to be around 5800 K it says that the Temp of the Corona region is much higher and can reach around 20 Million K. This might be because of a Stream of Particles or Highly excited/burning Stuff revolving around the Sun in such a high Speed just enough to keep in Orbit around the sun but not escape from its gravitational Pull like some other more excited Particles/Energy Matter. The core of the Sun has 15.7 Million K Temperature. While only a Fraction of the Energy emitted from the Sun is held within the Solar System the burnt out Energy escapes into Space travelling its Light Years just like Light from other Stars. Much is needed to explain and charter the paths of this energy. Regards Hi Studiot, Thanks. Yes, we are constantly receiving an abundant Solar Energy/Radiation on our Planet Earth ! While we can discuss about intra Earth Energy Pattern as one topic we are pondering over the overall Systemic changes as well. Considering that the Global Warming has much to do with the Temperature of Earth and its Variations we try to envisage what energy might get added and lost. As the whole of Solar System is hurtling along in its path with our Earth orbiting around the Sun while being carted along the Solar System Carrying along together the Moon [which catches up orbiting around the Earth while trying to fall towards the Earth as per Gravity Pull] and its atmosphere as well as Earth's Own Atmosphere and Surface Water etc, I think EARTH might lose or Gain Matter as well as Energy during its Journey [same goes to other Bodies as well] Albeit the change might be untraceable and in a Stable state of coordinated Motion it might be minimal with Steady Gravitational Fields and State of the Space traveled through.

How much is the Energy emitted by Sun ? Where does it go and what form it transforms itself - Matter or Energy Storage ? As of this moment Virginia US has around -2 Deg C while New Delhi has around 9 Deg C and Kashmir around - 9 Deg C and Bangalore has 20 Deg C ! We all know how much Energy it takes to Air Condition a Small area and Imagine what an amount of Variation in Energy and Temperature is involved in lifting the Temperatures or lowering it over such vast areas. No MAN is an ISLAND and similarly no Particle, Atom , Molecule , Body , City, Planet , Star System , Galaxy or Universe is so, in such a way that its Properties are not determined by the Rest of the Environment. Therefore the fact that Sun is Emitting so much Energy and Earth is absorbing part of it while emitting out itself certain energy in the process of the Sun and Earth everything else connected Hurtling through Space at an unknown Velocity in an unknown direction makes it almost impossible for us to treat any of these Entities as a SYSTEM and work out Equations within itself and decide on factors such as Entropy etc. We must take into consideration Everything Else too !! Therefore Assuming it to be a System talking about Global Warming etc I am not convinced about as we need to evaluate how much Energy is received by Earth, How much is dissipated out of it and what is the Effect of its Speed of travel through Space in this context !!! How much ?

You and I seem to agree on one thing that the Universe or Cosmos is Endless and Limitless. You say that there are Endless Matter but I say that as matter has this tendency to gravitate together the forces involved can so gravitate the matter around and leave the Space around Empty or Matter free. Please elaborate more on the exact meaning of Continuum, Energy and Wave.

good point

Hi, Why do you say there is no Empty Space ? Can you prove it ?? What I am asking is : If you have an Universe within some Boundaries [we seem to agree that a body of matter has to have bounds] then what is beyond this Bounds in any Dimensional Direction [Either X,Y,Z.. or T,E etc or known or unknown dimensions] - ie if you draw a Straight Line through in whatever way anyone can foresee or understand when this line crosses the Bound Vertically, Perpendicularly, Piercing through the Ceiling of this Bound, then What is beyond ? What is beyond it ??? Regards

Hi, Thanks. There is no ego involved. If at all something it is a crisp, unedited and ex tempo writing. Well my Claim about Nothingness and Endless Emptiness is easily understood and no need for any Equations. What is needed is to fit in the rest of the Matter withing this frame of Emptiness from a minute particle or Energy segment to the Heaviest Optimally Gravitated Body as well as the States and Changes of States of these non-Empty Matter. When I decide or find the Complete set of Equations I will certainly share it with all. Regards

Good Points ! +1

Well , at this stage I am working on my own in both Mathematical and Cosmology Fields to give wings to my own thoughts and not get restricted by existing Theories. Or else it will suppress my own line of thinking and intuitiveness. Sometimes I try and bring in my thinking in solving some Puzzles [where invariably heavy thinking is needed] into possible Generalization or Theories. For example We used a TRINARY SEARCH Algorithm in solving 39 Balls Problem better than a Binary Search Method. Similarly, here again the Property exhibited by Number 3 I noted from the Solution of another interesting Puzzle. We all know that 0 , 1 , 2 and 3 are the Bricks of Number Theories and 3 is on the Wall Dividing 0,1,2 and the rest 4.5.6 etc.. Like Fermat's theorem defines what is Possible with the Power 2 but not Possible for Powers 3 or more ! At this point I am looking at a possible link arising. Also if I add Walker's Equation too I can state : Every Possible Rational number can be expanded into a Sum of Powers of 2 Occurring Only Once and some Elements of the Matrix of Walker's Equation - perhaps occurring only once !

I think you misunderstood what I said. I know what Fermat's stated what you are quoting. That was his statement which needs to be proved or disproved.

Any Positive Natural Number N can be written as a positive sum of the Powers of 2 ! N = 2a + 2b ..... with as many terms as require where a , b , c etc are all Natural positive Numbers from [ 0,1,2,3 .....] These powers a, b, etc in the sequence will be PRESENT or ABSENT in the Equation only once. No repetition is required. This is nothing but a Binary Number representing the powers of 2 which add up to be equal to N. Similarly any N can be written as N = an additions or subtractions of Powers of 3 OCCURRING only once. N = 3a ± 3b ± 3c etc again a,b,c etc needing to appear only once ! Any number higher than 3 will not be able to produce such a Sum with their Powers Occurring only once ! Not possible to cover all N by 4a ± 4b ± 4c ....... or similarly by the powers of 5,6,7 ... or such higher numbers.

Thank you !

Thank you imatfaal !

imatfaal : Yes, your solution is correct and I have verified. I wish I had enlarged the text and read your second file earlier. I was busy creating the file / graphics to indicate my Solution. As I said earlier and as I see it now, there can be a few variations in the arrangement of weighings / balls. I CREDIT YOU WITH THE SOLUTION ! Well done !!