Question

show that \(a^8 + b^8 = c^8\) has no solution in positive integers

Answer 1

the general case n>= 3 was proved by wiles in the 90s

Answer 2

Wiles first announced his proof on Wednesday 23 June 1993 at a lecture in Cambridge entitled "Elliptic Curves and Galois Representations."

Answer 3

Yes that proof is like 102 pages long... but this specific case can be worked in less than a page. Fermat would work it in the margin of his law book ;)

Answer 4

I can show that a,b cannot be even

Answer 5

lol

Answer 6

cannot both*

Answer 7

i doodle in the margin of my books, well all over, a habit i didnt break since kindergarten lol

Answer 8

that will be a good start im sure

Answer 9

lol i still do that too

Answer 10

in fermat's words !
http://izquotes.com/quotes-pictures/quote-but-it-is-impossible-to-divide-a-cube-into-two-cubes-or-a-fourth-power-into-fourth-powers-or-pierre-de-fermat-61218.jpg

Answer 11

o i see

Answer 12

I think fermat did have the proof worked out

Answer 13

yes if we let any one of them 0, then there are infinitely many trivial solutions

Answer 14

other than 0 i mean

Answer 15

i know 1 is impossible but is 2 impossible too

Answer 16

oh i know did u use this formula
for
a^n+b^n=....

Answer 17

from geometric series

Answer 18

or binomial

Answer 19

also pythagorean triples..

Answer 20

i think @perl is trying pythagorean triples to show that a and b cannot be both even..