Discrete Math

For which values of $n$ can we subdivide an equilateral triangle into $n$ sub-triangles where each sub-triangle is also equilateral?

Prove that every integer greater than 1 can be written as the product of primes.

How many chicken nuggets can you buy exactly using denominations of 6, 9, and 20 pieces? Prove that you can buy exactly $n$ chicken McNuggets for all $n > 43$.

Find the sum of $n^2$ from $n = 1$ to $n = 5$.

Find the sum of $2^n$ from $n = 1$ to $n = 6$.

Find the sum of $3n + 2$ from $n = 1$ to $n = 5$.

Find the sum of the first 100 terms of the sequence given by $4n + 5$.

Calculate the sum of the first four terms of the sequence given by $\frac{3}{2}^{n-1}$.

Determine the sum of the infinite geometric sequence represented by $8 \left( \frac{2}{3} \right)^{n-1}$.

Translate the following predicate logic statement to English: "$\forall x \forall y ( C(x, y) \land R(x, y) \Rightarrow L(x, y) )$".

Get the sum of elements of a binary tree using recursion: Calculate root's value, and for each subtree, calculate the sum of its elements until reaching the base case where the node is null.

Get the maximum value in a binary tree using recursion: For each node, determine the maximum value in the left subtree and the right subtree, then return the maximum between root's value, leftMax, and rightMax.

Get the height of a binary tree using recursion: Calculate the height of both subtrees and return 1 plus the maximum between them.

Check if a specific value exists in a binary tree using recursion: Compare with the root's value, check in the left subtree, and in the right subtree.

Reverse a binary tree using recursion: Reverse its left subtree, reverse its right subtree, and swap the left node with the right node.

Give the pre-order, in-order, and post-order traversal of the tree below.