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At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

The whole neighborhood of any point y_i of an algebraic curve may be uniformly represented by a certain finite number of convergent developments in power series, ...

A general quintic equation a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 (1) can be reduced to one of the form y^5+b_2y^2+b_1y+b_0=0, (2) called the principal quintic form. Vieta's ...

SNTP(n) is the smallest prime such that p#-1, p#, or p#+1 is divisible by n, where p# is the primorial of p. Ashbacher (1996) shows that SNTP(n) only exists 1. If there are ...

An Achilles number is a positive integer that is powerful (in the sense that each prime factor occurs with exponent greater than one) but imperfect (in the sense that the ...

Exponentiation is the process of taking a quantity b (the base) to the power of another quantity e (the exponent). This operation most commonly denoted b^e. In TeX, the ...

Let P=a_1x+a_2x^2+... be an almost unit in the integral domain of formal power series (with a_1!=0) and define P^k=sum_(n=k)^inftya_n^((k))x^n (1) for k=+/-1, +/-2, .... If ...

A divisor d of a positive integer n is biunitary if the greatest common unitary divisor of d and n/d is 1. For a prime power p^y, the biunitary divisors are the powers 1, p, ...

Euler conjectured that at least n nth powers are required for n>2 to provide a sum that is itself an nth power. The conjecture was disproved by Lander and Parkin (1967) with ...

The nth root (or "nth radical") of a quantity z is a value r such that z=r^n, and therefore is the inverse function to the taking of a power. The nth root is denoted ...