The Great Depression is a period of time of American depression.

Let \(a,b \in \mathbb{Z}\), not both zero. \(\gcd (a,b)\) is the greatest value \(d\) such that \(d|a\), \(d|b\).

greatest common divisor is a linear combination

We can write \(\gcd (a,b) = as+bt\) for some \(s,t \in \mathbb{Z}\).

Let us define:

\begin{equation} S = \{am + bn: m,n \in \mathbb{Z}, am+bn > 0\} \end{equation}

We will first check that \(S\) is non-empty. To do so, let \(a\) be negative and \(b\) be positive. Then, set \(m = -1\), \(n = 1\). We can see that \(am + bn > 0\), satisfying the conditions of the set. In a similar manner, we can demonstrate that regardless of the choice of \(a, b\), \(S\) is non-empty.

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In this experiment, an efficient and accurate network of detecting automatically disseminated (bot) content on social platforms is devised. Through the utilisation of parallel convolutional neural network (CNN) which processes variable n-grams of text 15, 20, and 25 tokens in length encoded by Byte Pair Encoding (BPE), the complexities of linguistic content on social platforms are effectively captured and analysed. With validation on two sets of previously unexposed data, the model was able to achieve an accuracy of around 96.6% and 97.4% respectively — meeting or exceeding the performance of other comparable supervised ML solutions to this problem. Through testing, it is concluded that this method of text processing and analysis proves to be an effective way of classifying potentially artificially synthesized user data — aiding the security and integrity of social platforms.