The Heart of Mathematics: An Invitation...4th EditionBurger, Edward B. , Starbird, Michael Publisher: Wiley (WileyPLUS Products)ISBN: 9781119760054
The Heart of Mathematics: An Invitation...
Solutions for The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)
Problem 1MS:
PrimaI Instincts. List the first 15 prime numbers.Problem 2MS:
Fear factor. Express each of the following numbers as a product of primes: 6, 24, 27, 35, 120.Problem 3MS:
Odd couple. If n is an odd number greater than or equal to 3, can n+1 ever be prime? What if n...Problem 4MS:
Tower of power. The first four powers of 3 are 31=3,32=9,33=27, and 34=81. Find the first 10 powers...Problem 7MS:
Waking for a nonprime. What is the smallest natural number n, greater than 1, for which (123...n)+1...Problem 8MS:
Always, sometimes, never. Does a prime multiplied by a prime ever result in a prime? Does a nonprime...Problem 9MS:
The dividing line. Does a nonprime divided by a nonprime ever result in a prime? Does it ever result...Problem 10MS:
Prime power. Is it possible for an extremely large prime to be expressed as a large integer raised...Problem 11MS:
Nonprimes (ExH). Are there infinitely many natural numbers that are not prime? 1f so, prove it.Problem 12MS:
Prime test. Suppose you are given a number n and are told that 1 and the number n divide into n....Problem 13MS:
Twin primes. Find the first 15 pairs of twin primes.Problem 14MS:
Goldbach. Express the first 15 even numbers greater than 2 as the sum of two prime numbers.Problem 15MS:
Odd Goldbach (H). Can every odd number greater than 3 be written as the sum of two prime numbers? If...Problem 16MS:
Still the 1 (S). Consider the following sequence of natural numbers: 1111, 11111, 111111, 1111111,...Problem 17MS:
Zeros and ones. Consider the following sequence of natural numbers made up of 0s and 1s: 11, 101,...Problem 18MS:
Zeros, ones, and threes. Consider the following sequence of natural numbers made up of 0s, 1s, and...Problem 19MS:
A rough count. Using results discussed in this section, estimate the number of prime numbers that...Problem 20MS:
Generating primes (H). Consider the list of numbers: n2+n+17, where n first equals 1, then 2, 3, 4,...Problem 21MS:
Generating primes II. Consider the list of numbers: 2n1, where n first equals 2, then 3, 4, 5,...Problem 22MS:
Floating in factors. What is the smallest natural number that has three distinct prime factors in...Problem 23MS:
Lucky 13 factor. Suppose a certain number when divided by 13 yields a remainder of 7. What is the...Problem 24MS:
Remainder reminder (S). Suppose a certain number when divided by 13 yields a remainder of 7. If we...Problem 25MS:
Remainder roundup. Suppose a certain number when divided by 91 yields a remainder of 52. If we add...Problem 26MS:
Related remainders (H). Suppose we have two numbers that both have the same remainder when divided...Problem 27MS:
Prime differences. Write out the first 15 primes all on one Line. On the next line, underneath each...Problem 28MS:
Minus two. Suppose we take a prime number greater than 3 and then subtract 2. Will this new number...Problem 29MS:
Prime neighbors. Does there exist a number n such that both n and n+1 are prime numbers? If so, find...Problem 30MS:
Perfect squares. A perfect square is a number that can be written as a natural number squared. The...Problem 31MS:
Perfect squares versus primes. Using a calculator or a computer, fill in the last two columns of the...Problem 32MS:
Prime pairs. Suppose that p is a prime number greater than or equal to 3. Show that p+1 cannot be a...Problem 33MS:
Remainder addition. Let A and B be two natural numbers. Suppose that, when A is divided by n. the...Problem 34MS:
Remainder multiplication. Let A and B be two natural numbers. Suppose that the remainder when A is...Problem 35MS:
A prime-free gap (S). Find a run of six consecutive natural numbers, none of which is a prime...Problem 36MS:
Prime-free gaps. Using Mindscape 35, show that, for a given number, there exists a run of that many...Problem 37MS:
Three primes (ExH). Prove that it is impossible to have three consecutive integers, all of which are...Problem 38MS:
Prime plus three. Prove that if you take any prime number greater than 11 and add 3 to it the sum is...Problem 39MS:
A small factor. Prove that if a number greater than 1 is not a prime number, then it must have a...Problem 40MS:
Prime products (H). Suppose we make a number by taking a product of prime numbers and then adding...Problem 45MS:
Seldom prime. Suppose that x is a natural number and consider the associated number y given by...Problem 46MS:
A special pair of twins. A composite number x is the product of two twin primes p and q, in which...Browse All Chapters of This Textbook
Chapter 2.1 - CountingChapter 2.2 - Numerical Patterns In NatureChapter 2.3 - Prime Cuts Of NumbersChapter 2.4 - Crazy Clocks And Checking Out BarsChapter 2.5 - Public Secret Codes And How To Become A SpyChapter 2.6 - The Irrational Side Of NumbersChapter 2.7 - Get RealChapter 3.1 - Beyond NumbersChapter 3.2 - Comparing The InfiniteChapter 3.3 - The Missing Member
Chapter 3.4 - Travels Toward The Stratosphere Of InfinitiesChapter 3.5 - Straightening Up The Circ LeChapter 4.1 - Pythagoras And His HypotenuseChapter 4.2 - A View Of An Art GalleryChapter 4.3 - The Sexiest RectangleChapter 4.4 - Soothing Symmetry And Spinning PinwheelsChapter 4.5 - The Platonic Solids Turn AmorousChapter 4.6 - The Shape Of Reality?Chapter 4.7 - The Fourth DimensionChapter 5.1 - Rubber Sheet GeometryChapter 5.2 - The Band That Wouldn't Stop PlayingChapter 5.3 - Knots And LinksChapter 5.4 - Fixed Points, Hot Loops, And Rainy DaysChapter 6.1 - Circuit TrainingChapter 6.2 - Feeling Edgy?Chapter 6.3 - Plane Old GraphsChapter 6.4 - NetworkingChapter 7.1 - ImagesChapter 7.2 - The Infinitely Detailed Beauty Of FractalsChapter 7.3 - Between DimensionsChapter 7.4 - The Mysterious Art Of Imaginary FractalsChapter 7.5 - The Dynamics Of ChangeChapter 7.6 - Predetermined ChaosChapter 8.1 - Chance SurprisesChapter 8.2 - Predicting The Future In An Uncertain WorldChapter 8.3 - Random ThoughtsChapter 8.4 - Down For The CountChapter 8.5 - Drizzling, Defending, And DoctoringChapter 9.1 - Stumbling Through A Minefield Of DataChapter 9.2 - Getting Your Data To Shape UpChapter 9.3 - Looking At Super ModelsChapter 9.4 - Go FigureChapter 9.5 - War, Sports, And TigersChapter 10.1 - Great ExpectationsChapter 10.2 - RiskChapter 10.3 - Money MattersChapter 10.4 - Peril At The PollsChapter 10.5 - Cutting Cake For Greedy People
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