p.278, icon at Example 6# 3. (Problem A1 from the 1989 William Lowell Putnam Mathematics Competition.) Consider the sequence of integers(in base 10): 101, 10101, 1010101, 101010101, 10101010101,.... Prove that 101 is the only number in this sequencethat is prime. (Hint: Use place value to write each number in terms of the sum of its digits; for example, abcde =a10+ + b10³ + c10² + d10+ e. Then examine how the sum might be factored.)

To prove that 101 is the only prime number in the sequence…

Answered: p.278, icon at Example 6 # 3. (Problem…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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#4. Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i.
N. B. : This topic is from algorithm
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Module/Week 2 ASSIGNMENT (INPUT/OUTPUT)The number of permutations of a set of n items taken r at a time is given by the following formulan !⁄r !(n-r)!: where n! is the factorial of n, r! is the factorial of r, and (n-r)! is the factorial of the result of n-r. The factorial of a number n can be solved using the following formula: 〖n!=e〗^(-n) n^n√2πn. If there are 18 people in your class and you want to divide the class into programming teams of 3 members, you can compute the number of different teams that can be arranged using this formula (n !⁄r !(n-r)!). Write a C++ program that determines the number of potential team arrangements. You will need to use the double type for this computation. Use the Lab Template you set-up last week, proper formatting, and appropriate comments in your code. The output must be labeled clearly and formatted neatly. Submit C++ Programming Assignment 2 by 11:59 p.m. (ET) on Monday of Module/Week 2.
A 5-digit positive integer is entered through the keyboard, write a function to find reverse of the 5-digit number:(1) Without using recursion(2) Using recursion
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1.)I have to recursive with python language and was asked to do a buy 2 get 1 free where you have some amount of money(x) each item costs a given amount(y), for each 2 item you get 1 free, builda recursive solution to find out how many items you can buy for x amount of money. 2.) Buy M, get N free Then alter your first answer to allow for the user to enter any M and N for how many you need to buy to get free items

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