Tag Archives: quadratic

A simple proof of the quadratic formula

If you’re reading this blog you have probably memorized (or used to have memorized) the quadratic formula, which can be used to solve quadratic equations of the form But do you know how to derive the formula? Usually the derivation … Continue reading

Posted in algebra, proof | Tagged , , , , | 3 Comments

Triangunit divisors and quadratic reciprocity

Recall that the triangunit numbers are defined as the numbers you get by appending the digit 1 to the end of triangular numbers. Put another way, where denotes the th triangular number, and the th triangunit number. The challenge, posed … Continue reading

Posted in arithmetic, modular arithmetic, number theory, primes, proof | Tagged , , , , | 5 Comments