MathDB

We say that a positive integer

k

is tricubic if there are three positive integers

a, b, c,

not necessarily different, such that

k=a^3+b^3+c^3.

a) Prove that there are infinitely many positive integers

n

that satisfy the following condition: exactly one of the three numbers

n, n+2

and

n+28

is tricubic. b) Prove that there are infinitely many positive integers

n

that satisfy the following condition: exactly two of the three numbers

n, n+2

and

n+28

are tricubic. c) Prove that there are infinitely many positive integers

n

that satisfy the following condition: the three numbers

n, n+2

and

n+28

are tricubic.

Problem Statement