is an even integer then n square is .A Negative

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

A:

Q: what integer is closer to 6

A: given: the integer is six.

Q: find a Positive integern for which the equality holds %3D

A:

Q: "If a and b are positive integers, a divides b and b divides a, then a = b."

A: To Prove: '' If a and b are positive integers, a divides b and b divides a, then a = b''.

Q: Find a positive integer n for which the equality holds = 1 2

A:

Q: What can you conclude about the numbers m and n if X " = 7 and r is an even number and m and n are…

A: The number that is divisible by 2 is called the even number and the number that is not divisible by…

Q: Is the statement true or false? If an odd number is less than 15, then it is prime. False Give a…

A: We have to check

Q: Find the smallest integer value c and it's n, to show that 2n2 + 6n – 3 Oln –10) is an

A: Given:

Q: Show that if a positive integer is odd, then it's square is odd.

A: To show that if a positive integer is odd then its square is odd

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: When the smallest of three consecutive odd integers is added to four times the largest, it produces…

A:

Q: Use a direct proof to show that every odd integer is a difference of two squares. (For example: 1 =…

A: first we take a odd integer then we write in 2y+1 form then we transfer to difference of two…

Q: If x is an odd integer then 5x – 7 is an even integer.

A: 5 and x are odd integers. Multiplication of two odd integers is always odd. Hence, 5x is an odd…

Q: 2) The product of an even number and any other number is even.

A:

Q: use proof by contradiction to show that the number is irrational. 3

A: We have to prove 3 is irrational. Let us assume 3 is rational. So, it can be written in the form of…

Q: Prove that there is no triangular number which is one less than a multiple of 11.

A: Introduction: A triangular number is a positive integer that is the average of two integers. For…

Q: Are the irrational numbers closed under multiplication?

A: Use closure property.

Q: 11. Prove that if n is a perfect square, then n + 2 is not a perfect square.

A:

Q: 8. We will call the integer n doubly square if n is a perfect square and its number of positive…

A:

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

A:

Q: Luna told her friends that she was thinking of a number with the same digit in the ones and the…

A: To determine a number with the same digit in the ones and the thousands place (odd or even).

Q: If k is a positive integer, prove the k root of 6 is irrational

A: Given:Given that k is apositive integer.To find:The kth root of 6 is Irrational.

Q: Prove by contradiction that, if n is a positive integer which is not a perfect square, the sqrt(n)…

A:

Q: If the sum of any two integers is even, then so is their difference.

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: what is the largest integer less then square root of 375

A: Largest integer less than square root of 375

Q: 6 What is the smallest integer that makes the difference (3 X- 2greater than 1? Use estimation to…

A:

Q: If 48 ÷ x is a positive integer and x is an integer, what are the possible values of x?

A: We have to find interger

Q: A certain airline requires that the total outside dimensions (length + width + height) of a carry-on…

A: Given  l + b + h = 54 inch And Length = 2* height

Q: How many integer solutions to x1 + x2 + x3 + x4 = 32 are there for which x1≥6, x2 ≥5, x3 ≥3 and x4…

A:

Q: Show that square root P is irrational where P is prime by using contradiction.

A:

Q: Prove that if n is a perfect square, then n +2 is not a perfect square.

A:

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: Prove in a thoroughly written proof that for all integers a  and m, if a and m are the lengths of…

A: Recall the following. Pythagoras theorem: For any right triangle, the square of the hypotenuse is…

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: The sum of the squares of two odd integers is 1) Perfect 2) Prime 3) Not perfect

A: We will find out the required solution.

Q: Let n be an integer. If n is an even integer, then n5 + 20 is an even integer. is an irrational…

A:

Q: For which positive integers $n$ greater than or equal to 2 is $\sqrt[n]{a^{n}}=a$ always a true…

A: We need to check for all the values to get the result

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: se one) is an integer and x1} is an integer and x21} is an integer and l<x<4}

A: a. The roaster form is given as, 1,2,3,4........ The set-builder form is written as, xx is an…

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

A:

Q: Prove that 13,050.046 is not the square of a natural number.

A: Use the fact that an even number is perfect square the number is divisible by 4

Q: Suppose n is odd. Find the cube of n and divide it by 4. What possible remainders could occur? Check…

A: Solution

Q: How many integer solutions are there to 1 +X2+X3+X4+Xs=31 with

A: Given, x1+x2+x3+x4+x5=31 Number of Solutions when xi≥0 and xi&gt;0.

Q: be a positive number. Determine the values of p for which

A:

Q: Find a number that provides a counterexample to show that the given statement is false.

A: We have to find counter example for each of the given statement.

Q: the acdjainbaf square of As of 2.

A:

Q: the student noticed that if he writes a multiplication sign between the second and third digit of…

A:

Q: 4. The area of a parallelogram is 198 square units. If the base and the height of the parallelogram…

A: