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3^3 + 2^3 + 2^3

2^3 = 8

3^3 = 27

27 + 8 + 8 = 43

>>> math.pow(3,3) + math.pow(2,3) + math.pow(2,3)
43


Before last night, we had the sum of 3 cubes for every integer from 1-100 with the exception of 42.

In 1992, Roger Heath-Brown conjectured that all even numbers would have a sum of 3 cubes, this was proven last night for at 
least 1-100 for the 42.

Here is the famous equation:https://pad.yohdah.com/674/the-sum-of-3-cubes-solved-for-42/edit

42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3

Or in python:

>>> import math
>>> math.pow(-80538738812075974,3) + math.pow(80435758145817515,3) + math.pow(12602123297335631,3)


Dad, how do you even get a negative cube? Is it like a black hole???

So we learned the difference between conjecture and proofs.



Conjecture is something one or many people think ought to be true, but do not have complete proof,

While a Proof is something we have proven to be True!

Most proofs in mathmatics start out as Conjecture first, so you should be a thoughtful guy or gal!




3 + 3 = x - 3

what does x equal?

3 + 3 + 3 = x - 3 + 3

3 + 3 + 3 = x - 0

3 + 3 + 3 = x

9 = x






3 + 2 = x + 1

what does x equal?

3 + 2 - 1 = x + 1 - 1

3 + 2 - 1 = x + 0

3 + 2 - 1 = x

5 - 1 = x

4 = x


So lets test out our answer, by substituting 4 for x in our original equation.

3 + 2 = x + 1

3 + 2 = 4 + 1

5 = 5

does 5 equal 5, yes? then our answer of x = 4 is CORRECT!


So that is algebra! All it means is shifting around an equation to make it easier to ... SOLVE!!!






let us pretend we got the answer x = 5, plugging it into the original equation would give us:

3 + 2 = 5 + 1

or 

5 = 6

which is absolutely, positively False. 5 cannot equal 6, ever in math. So then we would know out answer was ... WRONG

kamahama big blackhole ballha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

vijetu"ow"