"There is no largest integer."

Q: Show that the square roots of two successive natural numbers greater than N2 differ by less than…

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Q: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

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Q: A Highest Common Factor of a, b is defined as: It is the greatest integer divisor of both a and b O…

A: Solution ---------------  Definition of HCF  ================ HCF (highest common factor) : The…

Q: Find the least positive integer that yields the remainders 1, 3, and 5 when divided by 5, 7, and 9,…

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Q: Show that 1+2+3+...+n= ("""). (";"').

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Q: How many perfect squares are there between 1,000,000 and 9,000,000?

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Q: What is an integer

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Q: Find the smallest positive integer that leaves a remainder of 1 when divided by 2, a remainder of 2…

A: Let N be such a number N=10a+9:  N+1 = 10a+10 N=9b+8: N+1 = 9b+9 N=8c+7: N+1 = 8c+8 N=7d+6 and so on…

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

A: It is given that the integers are from 1 through n, and no number appear more than 3 times.

Q: Find the largest value of n such that: > (6k – 8) < 3000 k=1

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Q: a) Assume that nothing is known about the percentage of adults who have heard of the brand (Round up…

A: Question: The brand manager for a brand of toothpaste must plan a campaign designed to increase…

Q: Use Polya’s Four Steps to solve the problem: How many perfect squares are between 1,000,000 and…

A: Find the number of perfect square between 1,000,000 to 9,000,000.   The four step of Polya’s is…

Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

Q: a) The square of any integer is either of the form 3k or 3k + 1.

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

Q: Show that if m is an integer then 3 divides m3−m.

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Q: The integers 77 and 105 are relatively prime.

A: Relatively Prime integers: Two integers mand n are called relatively prime if gcd(m,n)=1. Given two…

Q: a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. n= (Round…

A: a. The percentage of of passengers who prefer aisle seats is not known consider as 0.5, 99%…

Q: What is the smallest positive integer that has 6, 8, and 10 as factors?

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Q: A population of fruit flies is growing in such a way that each generation is 1.15 times as large as…

A: Given that: Population of fruit flies is 1.15 of the last generation in each new generation.Number…

Q: Prove that the sum of the squares of two odd integers cannot be the square of an integer.

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Q: What is the smallest integer n for which 25n&gt;512?

A: The provided expression is as follow:

Q: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

Q: Any n consecutive integers will include a number that is divisible by n.

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Q: 1. How many squares are in the figure?

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Q: (b) Find the sum of the first 110 positive odd integers.

A: Our Aim is to find the sum of the first 110 positive odd integers.

Q: The smallest primenumberis: 5) (3

A: The smallest prime number is.    2

Q: is an even integer then n square is .A Negative

A: Suppose n=m is an even integer.Since n=m , then n2=m2

Q: 1. Find the sum of the first 50 even positive integers.

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Q: Every odd prime number is greater than 2.

A: Given: "Every odd prime number is greater than 2." To find: Statement in the form "If p, then q"…

Q: what is the smallest integer greater than the square root of 117

A: Given, To find smallest integer  greater than the square root of 117

Q: Find the sum of all even integers from 10 to 500

A: Sum of all even integers from 10 to 500 .

Q: what is the smallest integer greater than the square root of 48

A: First perfect square after 48 is 49. First perfect square before 48 is 36 Square root of 49 is 7 and…

Q: 2(5) – 3(1 – 6) Is even integer?

A: If an integer is divisible by 2, then it is called an even integer. For example, 2,4,6 etc. are even…

Q: Show that the sum of the squares of the first n natural numbers is given by,S=(n(n+1)(2n+1))/6

A: We have to show that the sum of the squares of the first n natural numbers is given by S=nn+12n+16…

Q: 16. Find the positive integer that maximizes the sum of the numbers and its reciprocals?

A: Take integer and add them with his reciprocal Diifferenciate and get

Q: Find the largest negative integer leaves a remainder 2 when divided by 3, 5, and 12. (If it is not…

A: Let us  solve the question in the next step.

Q: Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width,…

A: Maximum volume will occur when the box is a cube with side length l.  Thus, 3l=84.  Calculate l:…

Q: countable in number, such that

A: Given : W=Iα:α∈A is a collection of open intervals, then there exists a sub-collection , say Ii :…

Q: Which of the following is an Integer ?

A: Given,           Ingeger number.

Q: There is no integer that has a reciprocal that is an integer.

A: As per the instructions, we will be answering only the first question. For (32), Notice that the…

Q: 4. Find The Three cube Meots of 1

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Q: Show that every odd integer is the sum of two consecutive integers

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Q: If n is an even integer, then 3n° is an even integer.

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Q: Find the sum of the integers from −20 to 256.

A: It is required to calculate the sum of integers from -20 to 256 that is:

Q: 3. Consider the checkerboard below. How many squares of all sizes appear on this checkerboard?

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Q: the acdjainbaf square of As of 2.

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Q: A population of fruit flies is growing in such a way that each generation is 1.15 times as large as…

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Q: Find the least natural number a with the property that the sum a + 2ā + 3a + ...+ 9a is the number…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.