Integers and Algebraic Expressions 2
... Late spring and summer rainfall in the Lake Okeechobee region in Florida is important to replenish the water supply for large areas of south Florida. Each bar in the graph indicates the number of inches of rainfall above or below average for the given month. Use the graph for Exercises 92–94. ...
... Late spring and summer rainfall in the Lake Okeechobee region in Florida is important to replenish the water supply for large areas of south Florida. Each bar in the graph indicates the number of inches of rainfall above or below average for the given month. Use the graph for Exercises 92–94. ...
![arXiv:math/0703236v1 [math.FA] 8 Mar 2007](http://s1.studyres.com/store/data/016433271_1-576581ae87603d2aee90a405a983700e-300x300.png)
Full text
... Fp~(5ip) is divisible by the prime p (p /= 5), where (5/p) is the Legendre's symbol, and it is well known that if p = 10k ± 1, then (5/p) = 1, therefore Fp_f is divisible by/?. So it is enough to prove the following lemma for the verification of the first part of Theorem 1: Lemma 1. If Fn is divisib ...
... Fp~(5ip) is divisible by the prime p (p /= 5), where (5/p) is the Legendre's symbol, and it is well known that if p = 10k ± 1, then (5/p) = 1, therefore Fp_f is divisible by/?. So it is enough to prove the following lemma for the verification of the first part of Theorem 1: Lemma 1. If Fn is divisib ...
Sequences, Series, and the Binomial Theorem
... This is “Sequences, Series, and the Binomial Theorem”, chapter 9 from the book Advanced Algebra (index.html) ...
... This is “Sequences, Series, and the Binomial Theorem”, chapter 9 from the book Advanced Algebra (index.html) ...
Exponential Sums and Diophantine Problems
... The above result, combined with numerical work on smaller values of n, has led to the determination of g(k) for all values of k. The precise formula is somewhat complicated to state, but the lower bound (1.2) is is fact attained for all but at most finitely many values of k. Refinements of the above ...
... The above result, combined with numerical work on smaller values of n, has led to the determination of g(k) for all values of k. The precise formula is somewhat complicated to state, but the lower bound (1.2) is is fact attained for all but at most finitely many values of k. Refinements of the above ...
Rational Numbers
... You began your study of numbers by counting objects around you. The numbers used for this purpose were called counting numbers or natural numbers. They are 1, 2, 3, 4, ... By including 0 to natural numbers, we got the whole numbers, i.e., 0, 1, 2, 3, ... The negatives of natural numbers were then pu ...
... You began your study of numbers by counting objects around you. The numbers used for this purpose were called counting numbers or natural numbers. They are 1, 2, 3, 4, ... By including 0 to natural numbers, we got the whole numbers, i.e., 0, 1, 2, 3, ... The negatives of natural numbers were then pu ...
