x and y are natural numbers.
Hello,
That's the sum of cubes
Well, well... The formula is
If you cant remember it, start from and develop it
Solving for it... ? Not impossible.
Note that
Since x and y are natural numbers, and are integers.
So the two factors will be a combination of the divisors of 208. For example 26 and 8 or 13 and 16 or...
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Try all the possible values for x+y among 1,2,4,8,13,16,26,52,104,208 ()
Then note that and is respectively among 208,104,...,2,1
Note that otherwise the product can't be large enough (check it )
If you need more explanations, do tell me. But as far as I can see, it will be a long way to do >.>
Factor and see what's leftMoo, about developing from : what do you do with and ?
Develop (x-y)^3 to get
So we know that x and y are positive -----> and
Obviously,
So you have 5 possibilities to test out (x-y stopping at 13).
For example. If then
Are there x and y such that and ? That's a linear system of equations
Exactly the same reasoning for the other possibilities !