Adhvaitha

Prove that the fraction \(\frac{21n+4}{14n+3}\) is irreducible for every natural number \(n\). To show that a fraction is irreducible, ...

In each of the following situations, indicate whether \(f = \mathcal{O}(g)\) (or) \(f = \Omega(g)\) or both (in which case \(f = \Theta(g...

This post contains the solution to the exercises of the book by  S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani named "Algorithms...

Suppose that \(a,b,c \in \mathbb{N}\). Prove each of the following: If \(a|b\) and \(b|c\), then \(a|c\). Since \(a|b\) and \(b|c\), w...

Theorem: (Euclid) There are infinitely many primes. Proof: This is a classic proof by contradiction. Assume that there are only finitel...