Please help with this deep learning!! Code in phyton

Note: All problems below are in the context of the MNIST data set, so you must load that as your testing and training set for all your models.

$1$ Breadth vs Depth

The most fundamental question when it comes to neural networks is 'how many nodes and how many layers'. I want to try to address the tradeoff in this section. Here, we'll be building networks to classify the MNIST data set, and look at the tradeoff in network shapes.

Problem $1$: A network to classify the MNIST data set will have $28**28=784$ input nodes, and $10$ output nodes $($one for each of the ten classes$).$ How many parameters would a linear softmax model with no hidden layers have? If a model had $k1$ hidden layers, and $m$ nodes in each hidden layer, how many parameters would it have? Call this function Params$(k,m).$

Note: I am looking for a mathematical function here in terms of $m$ and $k,$ not a coded solution.

Problem $2$: For a given number of parameters $P,$ what is the smallest and largest values of $k$ such that Params$(k,m)=P?$ Call this maxk value $k_P.$

Note: What should you do when $k_P$ is not an integer?

One difficulty in comparing network shapes is making the comparison fair. We can say that a comparison between a network of $k$ layers and $m$ nodes per layer, and a network of $k\text{'}$ layers is 'fair', if both networks have the same $($or approximately the same$)$ total number of parameters.