Intro to Elementary Number Theory Homework problem Find the smallest positive integer r such that(Note that 859 is prime.)Type your answer...2941 (mod 859).

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Please help explain for me. This question is confusing. If possible, please type answers. Thank you very much. (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
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Question 13 If two successive natural numbers have sum of squares equal to 113, what is the lower number? O 7 8. -8 -7
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(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?
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.
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Question 2 a) What numerical method would you use to find the missing value in the table below and explain your why? Year 1917 1918 1919 1920 1921 Export (in tons) 443 384 397 467 b) What assumption(s) would you make in finding the missing value?
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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Find the smallest positive integer r such that (Note that 859 is prime.) Type your answer... 2941 (mod 859).