[Math] Is it true that every positive integer is the sum of 18 fourth powers of integers

Question

Is it true that every positive integer is the sum of $18$ fourth powers of integers?

Does this means every positive integer $n = x_1^4+x_2^4+\cdots+x_n^4$ for some positive integer $n=18$?
Could you show me some example, I don't think I am understanding the question..( ex:
Explanation says $78$ can be written as a sum of $18$ fourth powers of integers, how? Can $1$ or $5$ be written as sum of $18$ fourth powers of integers?)

Thanks!

Answer 1

This is Waring's problem for $k=4$. The answer to your question is no because 79 requires 19 fourth-powers, as reported in the wikipedia page.