Intro to Elementary Number Theory homework problem. Suppose that n is a positive integer with the properties:• for any integers a, b, c,• n is not prime and• P10 |n, where p; is the ith prime (i.e., p₁ = 2, p2 = 3, ...).What is the smallest possible value of n?n abc implies that nlab or n|bc or n|ac

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Answered: Suppose that n is a positive integer…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please help m solve the questions below and kindly explain so I can be able to understand them by myself. Thanks a lot. (1) Think about the three-digit numbers that can be formed from the digits 1, 2, 3, 4and 5 without repetition.(a) How many of these are there?(b) How many of them are even?(c) How many of them are greater than 250? (2) Some of these are partitions and some aren’t. You don’t need to find the answer, youjust need to say why it is or isn’t a partition.(a) Breaking this class up into first-year students, second-year students, etc.(b) Breaking this class up into CS majors, math majors, etc.(c) Splitting up the numbers {1, 2, . . . 10} into even and odd(d) Splitting up the numbers {1, 2, . . . 10} into multiples of three, multiples of two,or neither
Part b is the one I need help with
c. Could you adapt Tylishia's method to other 183 49? If so, give at least two more examples subtraction problems, such as to the problem and show how to apply Tylishia's method in each 11. Tylishia says that she can calculate 324 - 197 by adding 3 to both numbers and calculating 327 – 200 instead. a. Draw a number line (which need not be perfectly to scale) to help you explain why Tylishia's method is valid. b. Explain in another way why Tylishia's method is valid. y -y ly, b- case. of
(a) The number N = 49,725 represents the ages of a group of teenagers multiplied together. How many teenagers are there and what are their ages? Explain. (b) Is there an integer N > 1 such that the square root, cube root, and fourth root of N are all integers, and if so, what is the smallest one?
Question 8b) I rounded to the nearest ten thousand and worked out that all of the numbers below will round to 420 000. The teacher marked it as incorrect as she rounded the numbers to the nearest thousand. By her textbook definition alone surely I was supposed to round to the nearest 10, 000? The number 420,000 has four zeros? Or am I wrong? Thanks for your time...
Problem 4. Let n be any positive integer. Prove that there exists a positive integer k (depending on n) such that the following list of n consecutive integers: k, k + 1, ·, k + n - 1 contains no prime number at all. = Hint. Use the factorial (but k n! is NOT the correct answer, start from this and try to see what are missing). You also need the 2-out-of-3 property of division.
please answer question 16 and 18 by using combination
Intro to Elementary Number Theory homework problem.
6. It is helpful to be able to think about very large numbers in terms of powers of 10. You should be familiar with many of these terms, but have you thought about how many 10's are multiplying each other? Here are some numbers to think about and examples of things that would be counted in these quantities. Fill in the proper power of 10. The first has been done for you. NUMBER POWER OF 10 EXAMPLE The distance between New York City and Boston is approximately 1 million feet. There are approximately 3 billion seconds in a century. There are 6 trillion miles in a light year, i.e. the distance light can travel in a year. There are approximately 1 quadrillion ants populating the earth at any time. There are approximately 8 quintillion grains of sand on all of the Earth's beaches. 1 million = 1,000 -1, 000 = 10 -10° = 10° 1 billion = 1,000 -1 million = 10' -10° = 1 trillion = (1 million) = (10")* = 1 quadrillion =1000-1 trillion = 1 quintillion = (1 billion)' =
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Suppose that n is a positive integer with the properties: • for any integers a, b, c, • n is not prime and • P10 |n, where p; is the ith prime (i.e., p₁ = 2, p2 = 3, ...). What is the smallest possible value of n? n abc implies that nlab or n|bc or n|ac