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…

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 21PE

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6.Coding-----""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.
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Exercise 1: (Design of algorithm to find greatest common divisor) In mathematics, the greatest common divisor (gcd) of two or more integers is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4. Why? Divisors of 8 are 1, 2, 4, 8. Divisors of 12 are 1, 2, 4, 6, 12 Thus, the common divisors of 8 and 12 are 1, 2, 4. Out of these common divisors, the greatest one is 4. Therefore, the greatest common divisor (gcd) of 8 and 12 is 4. Write a programming code for a function FindGCD(m,n) that find the greatest common divisor. You can use any language of Java/C++/Python/Octave. Find GCD Algorithm: Step 1 Make an array to store common divisors of two integers m, n. Step 2 Check all the integers from 1 to minimun(m,n) whether they divide both m, n. If yes, add it to the array. Step 3 Return the maximum number in the array.
Description Xiao Zhang is often distressed because there are too many things to arrange. Now he has n tasks at hand, and each task has a starting times, and an ending time e;. To complete a task, he must do it from the starting time to the ending time, and Xiao Zhang can only perform one task at the same time. Xiao Zhang wants to know how many tasks he can accomplish at most. Input The first line is an integer n (1sns300000), indicating the number of tasks Xiao Zhang has at hand. In the next n lines, each line contains two integers s₁, e¡ (1≤s;
#5.Incorrect gurantee downvote. 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.
3. Check whether a number is odd or even. If it is odd, find the square of the number. If it is even, find the cube of the number.

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