Question

Problem 2: (i) Let a be an integer. Prove that 2|a if and only if 2|a3....

Problem 2: (i) Let a be an integer. Prove that 2|a if and only if 2|a3.

(ii) Prove that 3√2 (cube root) is irrational.

Problem 3: Let p and q be prime numbers.

(i) Prove by contradiction that if p+q is prime, then p = 2 or q = 2

(ii) Prove using the method of subsection 2.2.3 in our book that if

p+q is prime, then p = 2 or q = 2

Proposition 2.2.3. For all n ∈ Z, if n2 is odd, then n is odd.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

a) consider fan=r7-2=0. Suppose e Paepe sot f(f/4)=0 Them by Rational root theorem, pl-2. and q11. possibilities for p are 1,-1,2,-2. - and that for & are 1 But if(1) = 4 f(-1)2 -3, f(2)= 6 F(-2)2 -20. Therefore fex)=0 Cannot have any rate 32 is real goot of f(n) zo. Hence 32 most be irrational.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Let n be an integer. Prove that n2 + 4n is odd if and only...
1. Let n be an integer. Prove that n2 + 4n is odd if and only if n is odd? PROVE 2. Use a table to express the value of the Boolean function x(z + yz).
Let p be an odd prime and let a be an odd integer with p not...
Let p be an odd prime and let a be an odd integer with p not divisible by a. Suppose that p = 4a + n2 for some integer n. Prove that the Legendre symbol (a/p) equals 1.
Let n be an integer, with n ≥ 2. Prove by contradiction that if n is...
Let n be an integer, with n ≥ 2. Prove by contradiction that if n is not a prime number, then n is divisible by an integer x with 1 < x ≤√n. [Note: An integer m is divisible by another integer n if there exists a third integer k such that m = nk. This is just a formal way of saying that m is divisible by n if m n is an integer.]
1. Prove that {2k+1: k ∈ Z}={2k+3 : k ∈ Z} 2. Prove/disprove: if p and...
1. Prove that {2k+1: k ∈ Z}={2k+3 : k ∈ Z} 2. Prove/disprove: if p and q are prime numbers and p < q, then 2p + q^2 is odd (Hint: all prime numbers greater than 2 are odd)
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also...
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also odd. 3.b) Let x and y be integers. Prove that if x is even and y is divisible by 3, then the product xy is divisible by 6. 3.c) Let a and b be real numbers. Prove that if 0 < b < a, then (a^2) − ab > 0.
4. Prove that if p is a prime number greater than 3, then p is of...
4. Prove that if p is a prime number greater than 3, then p is of the form 3k + 1 or 3k + 2. 5. Prove that if p is a prime number, then n √p is irrational for every integer n ≥ 2. 6. Prove or disprove that 3 is the only prime number of the form n2 −1. 7. Prove that if a is a positive integer of the form 3n+2, then at least one prime divisor...
This problem outlines a proof that the number π is irrational. Suppose not, Then there are...
This problem outlines a proof that the number π is irrational. Suppose not, Then there are relatively prime positive integers a and b for which π = a/b. If p is any polynomial let Ip= ∫0a/bp(x) sinx dx. i. Show that if p is non-negative and not identically 0 on [0,a/b] then Ip>0; ii. Show that if p and all of its derivatives are integer-valued at 0 and a/b then Ip is an integer. iii. Let N be a large...
(a) Let N be an even integer, prove that GCD (N + 2, N) = 2....
(a) Let N be an even integer, prove that GCD (N + 2, N) = 2. (b) What’s the GCD (N + 2, N) if N is an odd integer?
Prove the following: Let n∈Z. Then n2 is odd if and only if n is odd.
Prove the following: Let n∈Z. Then n2 is odd if and only if n is odd.
Prove the statement in problems 1 and 2 by doing the following (i) in each problem...
Prove the statement in problems 1 and 2 by doing the following (i) in each problem used only the definitions and terms and the assumptions listed on pg 146, not by any previous establish properties of odd and even integers (ii) follow the direction in this section (4.1) for writing proofs of universal statements for all integers n if n is odd then n3 is odd if a is any odd integer and b is any even integer, then 5a+4b...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT