According to http://arxiv.org/vc/arxiv/papers/0901/0901.1857v1.pdf
… in Proposition 2, we prove that each integer-sided triangle can have at most two medians of integer length
Can you disprove this claim?
That is, find an integer-sided triangle with all three median lengths being integral.
Formulas for median length
To find (m, n) so that C(m,n) is a product of all prime numbers ≤ m
It appears that the product of the primes is increasing faster than the possible combination numbers.
I don’t know if we could have another case where the combinations would equal the product of primes.
I don’t have the proof.
To find (m, n) so that C(m,n) is a product of consecutive prime numbers
To find a sum of four or more consecutive cubes – not starting with 1 – giving us the square of an integer
From Republic of Math :
From Derek :
From Max Alekseyev:
A126200 Numbers n such that n^2 is a sum of consecutive cubes larger than 1
David Radcliffe sent me a link to “primitive solutions to x^2 + y^3 = z^7″
Find the arrangement of the array :