# Elementary techniques in a simple case of Vinogradov’s mean value theorem

FirstCaseofVMVT

In the above pdf, I explore the first nontrivial case of Vinogradov’s mean value theorem. That is, I seek to bound solutions to the simultaneous systems $x_1^j + x_2^j + x_3^j = y_1^j + y_2^j + y_3^j$ for $j = 1,2$, where all the variables are integers in $\{1 , \ldots , N\}$. This is much easier (still nontrivial) than the general case, due to the existence of helpful symmetries.