How many digits does the smallest positive integer K have, while satisfying all of the following conditions: • K is an odd number • K is a cube • K is a square • K is divisible by 12 different prime numbers

How many digits does the smallest positive integer K have, while satisfying all of the following conditions: • K is an odd number • K is a cube • K is a square • K is divisible by 12 different prime numbers

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Prove by mathematical induction that the sum of cubes of three consequtive positive integers n is…

Q: How many integers from 1 to 700 (inclusive) are divisible by the factors of 70 greater than 1?

Q: Suppose that n is a positive integer with the properties: • for any integers a, b, c, • n is not…

Q: How many three-digit numbers can be made from the digits 0,1,2, 3 and 4, used at most once each, if…

A: In today's digital age, cybersecurity has become an essential concern for individuals,…

Q: If a and b are two distinct prime numbers, then the greatest common divisor of a and b is O ab

Q: Show that a positive integer N is divisible by 7 if and only if the difference between twice the…

A: We have to show that a positive integer N is divisible by 7 if and only if the difference between…

Q: Determine whether the following statement is true or false. Justify your answer with a proof or a…

Q: (a) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that…

A: Any number which has 0 or 5 in the unit place is divisible by 5. Case 1: when unit digit is 0 The…

Q: Covert to an equalivent statement to a universal statement:"6 is the smallest postive integer that…

A: According to the given information, It is required to write the statement into universal statement.…

Q: Find the distance between K and L on the number line below. ←++ -12 -11 -10 -9 -8 Distance: + -7 -6…

A: Distance between K and L is

Q: How many integers in {1, 2,..., 100} are not divisible by 7 or 5? (Give the exact number)

A: Find the number of integers in 1,2,...,100 which are not divisible by 7 or 5.

Q: Find the GCD and the LCM for each of the following groups of numbers using the prime factorization…

A: We have to find GCD and LCM in parts a),b),c) and d) GCD is the largest number that is the factor…

Q: Do you thinkthat there are infinitely many primes of the n -1

A: there are infinitely many primes of the n -1 Explain the above statement

Q: Show that if p is a prime number, a and b are positive integers and p | ab, then p | a or p | b.

A: The objective is to prove that if p is a prime number, a and b are positive integers and p | ab,…

Q: Prove that if 7 divides n with remainder 1, 7 divides n² + 2n + 7 with remainder 3.

A: Given, if 7 divides n with remainder 1. We have to prove that 7 divides n2+2n+7 with remainder 3.

Q: If n is any integer then n and n5 will have? (mcq) A. Both are divisible by 5 B. 10s place is…

Q: Use the Fermat's method to express each number in canonical prime factorization. 1. 229 2. 383 3.…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: If k is a positive integer, what is the remainder when (k+ 2)(k³ - k) is divided by 6? aburitowd ned…

Q: let n be an integer solution to the equation n2+an-b=0 (n>7) if the representation of a in base n is…

Q: Find the smallest five consecutive composite integers.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: a = ? b = ? c = ? d = ? e = ?

Q: 215 = 32, 768. How many numbers between 0 and 215 are the sum of exactly three powers of 8? Each…

A: We need to find the how many numbers between 0 and 215=(23)5=85 such that the sum of exactly three…

Q: For each natural number n A, = (-→ 3+n U-1 Find UneN An and NnEN An

Q: which of the following defines the positive integers divisible by both 3 and 4? Select one: O a. 12…

A: Explanation of the solution is given below...

Q: А. If p 2q 5 is a prime number, prove that p2-q? is divisible by 3.

Q: 2. Factor 10+1 into a product of primes for k = 1,2,3,4,5.

Q: For every natural number n, one of n-1, n, or n+1 is a multiple of 3

A: The following two steps are used to prove a statement P(n) by the principle of mathematical…

Q: Which of the following is an Integer ?

A: Given, Ingeger number.

Q: 4q, Prove the following statement: Every integer n has the form n = n = 4q+1, n = 4q+2, or n = 4q+3…

A: We have to prove that every integer n has the form n=4q, n=4q+1, n=4q+2, or n=4q+3 for some integer…

Q: How many zero divisors are in Z,, where n = 32547?

Question

How many digits does the smallest positive integer K have, while satisfying all of the following conditions:
• K is an odd number
• K is a cube
• K is a square
• K is divisible by 12 different prime numbers

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Introduction

VIEW

Solution

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

How many integers from 1 to 500 are divisible by at least one of the numbers 3, 4, 5?
Prove the statements: Let n be an odd positive integer. Then the sum of n consecutive integers is divisible by n.
If n is 0 what is 8n
(1) Let p be a prime number. Show that for any integer a the greatest common divisor of p and a is either p (if pla) or is 1 (if p does not divide a).
In cleaning out your old desk, you find a whole bunch of 3¢ and 7¢ stamps. Can you exactly 11¢ of postage? Can you make exactly 19¢ of postage? What is the largest am of postage you cannot make? eware of Patterns! 9 ST M Find the largest eight-digit number made up of the digits 1, 1, 2, 2, 3, 3, 4, and 4 sucl the 1's are separated by one digit, the 2's are separated by two digits, the 3's by three digits, and the 4's by four digits. Book Pro Problem 15 JA Problem 16 17 & Next: Careful Use of L
How many numbers have digits which are all ”1”s and ”2”s, and thedigits add up to 8? A few such numbers are 12212, 112121, and 112121. (HINT: breakthe list into cases and count each one. You can count them by hand, but you will savea lot of time if you apply the right formula.)
Find the smallest positive integer N that satisifies all of the following conditions N is a square N is a cube N is an odd number N is divisible by twelve different prime numbers How many digits does this number have ?
Find the GCD and the LCM for each of the following groups of numbers using the prime factorization method. a. 132 and 504 b. 33 and 1815 c. 96, 900, and 630 d. 500 and 600 a. GCD(132,504) = | LCM(132,504) = b. GCD(33,1815) = LCM(33,1815)= c. GCD(96,900,630) = LCM(96,900,630) = d. GCD(500,600) = LCM(500,600) =