Algebra & Number Theory formula — definition, units and applicable conditions

found 4formulas · currently displayed 4Articles Explanation · Unit · Applicable conditions

Algebra & Number Theory

root formula for a quadratic equation of one variable

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

solves for the zeros of a quadratic polynomial; the discriminant determines the number of real roots.

Algebra & Number Theory

(a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k

Expands binomial sums raised to integer powers into finite sums.

Algebra & Number Theory

S_n=a\frac{1-r^n}{1-r}

Calculate the sum of the first n terms whose leading term is a and whose common ratio is r.

Algebra & Number Theory

a^{\varphi(n)}\equiv1\pmod n

An integer that is relatively prime to the modulus, and its power has a periodic structure in the modular sense.