Question: Prove: If k is an even integer, then k 2 1 is odd.

Prove:

If k is an even integer, then k2 1 is odd.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

(a) [worth 1 point] Prove that -k = (-1)"( (k+n-1) k-1 for all k 2 1 and n 2 0. (b) [worth 1 point] What is the generating function of the sequence ao, a1, a2, ... where an = (-1)" (k+n-1) k-1 for...

Q:

Show that as k goes from 0 to the ratios ax = b(k; n, p)/p(k; 2) first increase, then decrease, reaching their maximum when k is the largest integer not exceeding 2 +1.

Q:

Please answer with solution thanks Learning Task 3 A. Prove the following using Direct Proof 1. Given: Odd and even integers Prove: the sum of odd and even integers is odd integer Solution: Supply...

Q:

Answer 6.1, 6.3, 6.4, 6.6, 6.9, 6.14, 6.15, 8.1, 8.5, 8.8, 8.13, and 8.19 Problem 6.1 Show that there exist integers m and n such that 3m + 4n = 25. Problem 6.2 Show that there is a positive integer...

Q:

Problem 2: Consider the set of integers. 1. Use a direct proof to show that the sum of two even integers is even. 2. Prove that if m+ n and n + p are even integers, where m, n, and p are integers,...

Q:

Direct Proofs Prove the following via a Direct Proof: 1.1 The square of an even natural number is even. 1.2 The square of an odd natural number is odd. 1.3 If n is a positive integer, then the...

Q:

20) Prove that if n and m are odd integers, then n - m is an even integer. Proposed proof: 2k + 1 - 2j + 1 = 2, so it is always odd. i safarl File Edit View History Bookmarks Window Help G) -r 'e' Q...

Q:

Prove each statement. (a) For every integer n, if n2 is an odd, then n is odd. (b) For every integer x, if x2 -2x +7 is even, then x is odd. (c) If x and y are real numbers and x + y is irrational,...

Q:

Sec 4 . 2 : # 2 3 Using the properties of even and odd integers listed in Example 4 . 2 . 3 , prove or disprove: If k is any even integer and m is any odd integer, then ( k + 2 ) 2 - ( m - 1 ) 2 is...

Q:

Question 21 18 pts Prove algebraically that for all integers x, the expression x3 + 3x2 + 5x has the same parity as x. (Remember that the parity of an integer refers to whether it's even or odd.)...

Q:

Consider a general topology (that is, not the specific network shown above) and a synchronous version of the distance-vector algorithm. Suppose that at each Iteration, a node exchanges its distance...

Q:

A soft-drink firm is evaluating an investment in a new type of canning machine. The company has already determined that it will be able to fill more cans per day for the same cost if the new machines...

Q:

An experience rating, or merit rating a . adjusts the FUTA contributions due to an unfavorable employment record. b . adjusts an employer's SUTA contributions due to a favorable employment record. c...

Q:

The Pants Company had the following transactions for their business: a.) On August 20th, 2020. The Pants Comp on account with (terms of 2/10,n/30 ). The gooas cost $2,500. b.) On August 22, 2020....