Please explain all the steps and this is for discrete math. and also do the rese

Question

Please explain all the steps and this is for discrete math. and also do the research part of the assignment too

1. A Pythagorean triple consists of three naturals i,j, and k, each greater than 0, such that i2+j2k2 one example is (3, 4,5). It has been proven that there exist infinitely many Pythagorean triples. Prove or disprove that there exist three naturals i, j, and k, each greater than 0, such that i3 += k3 Hints: (1) Do some research before attempting this question. Cite your references. (2) Boldly go where no man or woman has gone before.

Explanation / Answer

it is not possible . as please see below proof using mathematics:

use formula

a3+b3= (a+b)(a2 + b2- ab)

now for RHS to be a cube of any number following should hold true.

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two

please see references in comments

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