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"