introduction to functional equations

... Despite being such a rich subject, this topic does not fit perfectly into any of the conventional areas of mathematics and thus a systematic way of studying functional equations is not found in any traditional book used in the traditional education of students. Several good books on the topic exist ...

... Despite being such a rich subject, this topic does not fit perfectly into any of the conventional areas of mathematics and thus a systematic way of studying functional equations is not found in any traditional book used in the traditional education of students. Several good books on the topic exist ...

of integers satisfying a linear recursion relation

... if it can be factored into an irreducible quadratic factor and a linear factor, we shall say that it is of "type [2,1]" and so on. In any case, the factorization is unique; denote the roots which correspond to linear factors by small italic letters a, b, c and the roots which correspond to irreducib ...

... if it can be factored into an irreducible quadratic factor and a linear factor, we shall say that it is of "type [2,1]" and so on. In any case, the factorization is unique; denote the roots which correspond to linear factors by small italic letters a, b, c and the roots which correspond to irreducib ...

Families of elliptic curves of high rank with nontrivial torsion group

... to Z/2Z × Z/2Z. In order to obtain such curves we will apply the following method due to J.-F. Mestre [Mes1]. Let X, X1 , X2 , X3 , X4 be five indeterminates and K = Q(X1 , X2 , X3 , X4 ). Q4 Let P ∈ K[X] be the polynomial P (X) = i=1 (X − Xi ) = X 4 + c3 X 3 + c2 X 2 + c1 X + c0 . It may be written ...

... to Z/2Z × Z/2Z. In order to obtain such curves we will apply the following method due to J.-F. Mestre [Mes1]. Let X, X1 , X2 , X3 , X4 be five indeterminates and K = Q(X1 , X2 , X3 , X4 ). Q4 Let P ∈ K[X] be the polynomial P (X) = i=1 (X − Xi ) = X 4 + c3 X 3 + c2 X 2 + c1 X + c0 . It may be written ...

Unit 1: Extending the Number System

... An exponent is a quantity that shows the number of times a given number is being multiplied by itself in an exponential expression. In other words, in an expression written in the form ax, x is the exponent. So far, the exponents we have worked with have all been integers, numbers that are not fract ...

... An exponent is a quantity that shows the number of times a given number is being multiplied by itself in an exponential expression. In other words, in an expression written in the form ax, x is the exponent. So far, the exponents we have worked with have all been integers, numbers that are not fract ...