MethodMath Math Questions and Answers

I have a trig final next week and Im drowning in identities.

Theres like 50 of them:

• Pythagorean identities
• Angle addition formulas
• Double angle formulas
• Half

Consider the Diophantine equation

where $p$ is a prime and we seek non-trivial integer solutions $(x,y,z) \in \mathbb{Z}^3 \setminus \{(0,0,0)\}$.

By a classical descent argument using the fact that $\mathbb{Q}(\sqrt{-3})$ has class

This trick is all over Instagram:

To multiply $23 \times 47$:

Total: $800 + 140 + 120 + 21 = 1081$

But isnt this just FOIL? $(20+3)(40+7)$ expanded? So its not really a "trick" but

I am trying to understand the computation

Using the covering map $p: \mathbb{R} \to S^1$ given by $p(t) = e^{2\pi i t}$, I can see that each loop $\gamma: [0,1] \to S^1$ based at $1$ lifts uniquely to

In school they told us "you cant divide by zero" but they never explained WHY.

Like if you divide a number by a really small number you get a really

I'm studying A-Level calculus and I can state the Mean Value Theorem:

If $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$, then there exists $c \in (a,b)$ such that:

In the $8 \div 2(2+2)$ debate, I keep hearing about "implicit multiplication" or "multiplication by juxtaposition" having higher priority than normal multiplication.

The argument is that $2(2+2)$ means $2$ is implicitly multiplied

I'm studying combinatorics and I'm stuck on a problem involving permutations with restrictions.

Problem: \"How many ways can 5 distinct mathematics books and 3 distinct physics books be arranged on