6. Prove that if a and b are odd integers, then a2 is divisible by 8....

Question

Question

6. Prove that if a and b are odd integers, then a2 is divisible by 8. 7. Prove that if a is an odd integer, then ta + (a + 2)

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

O let a and b ae odd integer Ta shou that d 1s disible by 9 Here k, and k kif kıtí). is are consecuH ve numberrs even С anru GOLDEN TOUCH a is an add integen To move 1 0+ Cat2 ca+ is divisible b |2 onider ata 2 12-m aCd is divisible by l2

Add a comment

Answer 2

Similar Homework Help Questions

(6) Use a proof by contrapositive to prove for all integers a, b and c, if...

(6) Use a proof by contrapositive to prove for all integers a, b and c, if a t be then à f 6. (7) Prove using cases that the square of any integer has the form 4k or 4k +1 for some integer k. (8) Prove by induction that 32n -1 is divisible by 8.
13. Prove that for all integers b, if b is odd then b is odd 13. Prove that for all integers b, if b is odd then b is odd

13. Prove that for all integers b, if b is odd then b is odd 13. Prove that for all integers b, if b is odd then b is odd
Assignment 6 1. Prove by contradiction that: there are no integers a and b for which...

Assignment 6 1. Prove by contradiction that: there are no integers a and b for which 18a+6b = 1. 2. Prove by contradiction that: if a,b ∈ Z, then a2 −4b ≠ 2 3. Prove by contrapositive that: If x and y are two integers whose product is even, then at least one of the two must be even. Make sure that you clearly state the contrapositive of the above statement at the beginning of your proof. 4. Prove that...

1) Let n and m be positive integers. Prove: If nm is not divisible by an...

1) Let n and m be positive integers. Prove: If nm is not divisible by an integer k, then neither n norm is divisible by k. Prove by proving the contrapositive of the statement. Contrapositive of the statement:_ Proof: Direct proof of the contrapositive
please answer questions #7-13 7. Use a direct proof to show every odd integer is the...

please answer questions #7-13 7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
prove the product of 4 consecutive integers is always divisible by 24 using the principles of math induction

prove the product of 4 consecutive integers is always divisible by 24 using the principles of math induction. Could anyone help me on this one? Thanks in advance!Sure For induction we want to prove some statement P for all the integers. We need: P(1) to be true (or some base case) If P(k) => P(k+1) If the statement's truth for some integer k implies the truth for the next integer, then P is true for all the integers. Look at...

Problem of the Week #4 1. An integer bis said to be divisible by an integer...

Problem of the Week #4 1. An integer bis said to be divisible by an integer a 0, in symbols ab. if there exists some integer c such that b = ac. In other words, b is divisible by a if a goes into b with no remainder. For example, 30 is divisible by 5 (in symbols, 5 30 ) because 30 = 5 x 6. Problem of the Week: The following integers are all divisible by 31: 28272, 27683,...
Prove by induction that the sum of any sequence of 3 positive consecutive integers is divisible...

Prove by induction that the sum of any sequence of 3 positive consecutive integers is divisible by 3. Hint, express a sequence of 3 integers as n+(n+1)+(n+2).
Prove that a(a + 1)(2a + 1) is divisible by 6 for integer a using a...

Prove that a(a + 1)(2a + 1) is divisible by 6 for integer a using a quicker proof of this, based on the observation that 6 I m (6 divides m) if and only if 2 I m (2 divides m) and 3 I m (3 divides m). Please use modulo congruences.

How would someone prove that for all nonnegative in- tegers n, the number 6 1 is divisible by 5? ...

Can someone solve this along with steps and explanations? How would someone prove that for all nonnegative in- tegers n, the number 6 1 is divisible by 5? Would it work to just check to see if the statement is true for n 0, 1, 2, 3, 4,5? Surely if a pattern is noticed for the first few cases, it should work for all cases, or? Day 1. Consider the inequality n 10000n. Assume the goal is to prove that...

6. Prove that if a and b are odd integers, then a2 is divisible by 8....

Homework Answers

Add Answer to:
6. Prove that if a and b are odd integers, then a2 is divisible by 8....

Post as a guest

Earn Coins

(6) Use a proof by contrapositive to prove for all integers a, b and c, if...

13. Prove that for all integers b, if b is odd then b is odd 13. Prove that for all integers b, if b is odd then b is odd

Assignment 6 1. Prove by contradiction that: there are no integers a and b for which...

1) Let n and m be positive integers. Prove: If nm is not divisible by an...

please answer questions #7-13 7. Use a direct proof to show every odd integer is the...

prove the product of 4 consecutive integers is always divisible by 24 using the principles of math induction

Problem of the Week #4 1. An integer bis said to be divisible by an integer...

Prove by induction that the sum of any sequence of 3 positive consecutive integers is divisible...

Prove that a(a + 1)(2a + 1) is divisible by 6 for integer a using a...

How would someone prove that for all nonnegative in- tegers n, the number 6 1 is divisible by 5? ...

6. Prove that if a and b are odd integers, then a2 is divisible by 8....

Homework Answers

Add Answer to: 6. Prove that if a and b are odd integers, then a2 is divisible by 8....

Post as a guest

Earn Coins

Add Answer to:
6. Prove that if a and b are odd integers, then a2 is divisible by 8....