3^3+4^3+5^3 = 6^3
1^3+6^3+8^3 = 9^3
6^3+8^3+10^3 = 12^3
2^3+12^3+16^3 = 18^3
9^3+12^3+15^3 = 18^3
3^3+10^3+18^3 = 19^3
7^3+14^3+17^3 = 20^3
12^3+16^3+20^3 = 24^3
4^3+17^3+22^3 = 25^3
3^3+18^3+24^3 = 27^3
18^3+19^3+21^3 = 28^3
11^3+15^3+27^3 = 29^3
15^3+20^3+25^3 = 30^3
4^3+24^3+32^3 = 36^3
18^3+24^3+30^3 = 36^3
6^3+20^3+36^3 = 38^3
14^3+28^3+34^3 = 40^3
2^3+17^3+40^3 = 41^3
6^3+32^3+33^3 = 41^3
21^3+28^3+35^3 = 42^3
16^3+23^3+41^3 = 44^3
5^3+30^3+40^3 = 45^3
3^3+36^3+37^3 = 46^3
27^3+30^3+37^3 = 46^3
24^3+32^3+40^3 = 48^3
8^3+34^3+44^3 = 50^3
29^3+34^3+44^3 = 53^3
6^3+36^3+48^3 = 54^3
12^3+19^3+53^3 = 54^3
27^3+36^3+45^3 = 54^3
36^3+38^3+42^3 = 56^3
9^3+30^3+54^3 = 57^3
15^3+42^3+49^3 = 58^3
22^3+30^3+54^3 = 58^3
21^3+42^3+51^3 = 60^3
30^3+40^3+50^3 = 60^3
7^3+42^3+56^3 = 63^3
33^3+44^3+55^3 = 66^3
22^3+51^3+54^3 = 67^3
36^3+38^3+61^3 = 69^3
7^3+54^3+57^3 = 70^3
14^3+23^3+70^3 = 71^3
8^3+48^3+64^3 = 72^3
34^3+39^3+65^3 = 72^3
36^3+48^3+60^3 = 72^3
12^3+51^3+66^3 = 75^3
38^3+43^3+66^3 = 75^3
12^3+40^3+72^3 = 76^3
31^3+33^3+72^3 = 76^3
39^3+52^3+65^3 = 78^3
28^3+56^3+68^3 = 80^3
9^3+54^3+72^3 = 81^3
25^3+48^3+74^3 = 81^3
4^3+34^3+80^3 = 82^3
12^3+64^3+66^3 = 82^3
19^3+60^3+69^3 = 82^3
28^3+53^3+75^3 = 84^3
42^3+56^3+70^3 = 84^3
54^3+57^3+63^3 = 84^3
50^3+61^3+64^3 = 85^3
20^3+54^3+79^3 = 87^3
26^3+55^3+78^3 = 87^3
33^3+45^3+81^3 = 87^3
38^3+48^3+79^3 = 87^3
21^3+43^3+84^3 = 88^3
25^3+31^3+86^3 = 88^3
32^3+46^3+82^3 = 88^3
17^3+40^3+86^3 = 89^3
10^3+60^3+80^3 = 90^3
25^3+38^3+87^3 = 90^3
45^3+60^3+75^3 = 90^3
58^3+59^3+69^3 = 90^3
6^3+72^3+74^3 = 92^3
54^3+60^3+74^3 = 92^3
32^3+54^3+85^3 = 93^3
15^3+50^3+90^3 = 95^3
19^3+53^3+90^3 = 96^3
48^3+64^3+80^3 = 96^3
45^3+69^3+79^3 = 97^3
11^3+66^3+88^3 = 99^3
16^3+68^3+88^3 = 100^3
35^3+70^3+85^3 = 100^3
. . .robert Ihnot said:Euler's Conjecture is that it took n nth powers to equal an an nth power. But it was shown in 1966--largely by accidential discovery that four fifth powers will do:
[tex] 27^5+84^5+110^5+135^5 = 144^5.[/tex]
Char. Limit said:
TimGrebin said:The earlier confusion about the cube rooting, I think you have it wrong.
You have
a3 + b3 = c3
To cube root 'a', you are effectively multiplying it by a1/3 , to do this you would have to also multiply b and c by a1/3. Doing the same for b and c, you'd end up with an equation looking like this:
ab1/3c1/3 + ba1/3c1/3 = ca1/3b1/3
This does work.iamafigment said:(11/3)3 + (11/3)3 = (21/3)3
Why won't that work?
This doesn't work.iamafigment said:As I understand it, you are looking for values for a,b, and c where
a+b=c AND a^3 + b^3 = c^3
How about this?
a=cube rt 1
b=cube rt 1
c=cube rt 2
disscombobila said:I have heard of this referred to as Pythagora's second theorem. It is said to be one of the most difficult and yet unsolved math problems known. It is stated, A cubed plus B cubed cannot equal C cubed and finding the proof for this has eluded the best mathematicians for centuries. According to lore, Pythagoras had the proof written down on a corner of a papyrus but some how the corner went missing. Props to anyone who can find it. I believe some think it may have to do with a Torus Knot.
iansinclair said:Hi guys this proof does exist beyond any reason of doubt and it proves itself.
a^n+b^n=c^n rings true as well. Obviously i cannot divulge much about this but WC was stabbing in the wrong direction as such.
as mentioned the proof proves itself.
The only thing WC got right was that it is a curve.
Hopefully i find the right place to publish one day but till then my safe is a good place as my Son and I had painstakingly worked our own logbook on this making it a mathematical equation that works and applies to modern maths.
Oh b t w you use fractions as well in the nth root as it is a great necessity.
Ian