Question

Prove that there are no pairs of integers (a,b) in Z^2 such that a^2-4b=2

Prove that there are no pairs of integers (a,b) in Z^2 such that a^2-4b=2

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

Homework Answers

Answer #1

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
Let Z be the integers. (a) Let C1 = {(a, a) | a ∈ Z}. Prove...
Let Z be the integers. (a) Let C1 = {(a, a) | a ∈ Z}. Prove that C1 is a subgroup of Z × Z. (b) Let n ≥ 2 be an integer, and let Cn = {(a, b) | a ≡ b( mod n)}. Prove that Cn is a subgroup of Z × Z. (c) Prove that every proper subgroup of Z × Z that contains C1 has the form Cn for some positive integer n.
Prove: Let a and b be integers. Prove that integers a and b are both even...
Prove: Let a and b be integers. Prove that integers a and b are both even or odd if and only if 2/(a-b)
Prove or disprove that there do not exist z, y, and z are positive integers such...
Prove or disprove that there do not exist z, y, and z are positive integers such that X7 - Y5 = Z4
Prove that the ring of integers of Q (a number field) is Z
Prove that the ring of integers of Q (a number field) is Z
3. Prove or disprove: For integers a and b, if a|b, then a^2|b^2. 4. Suppose that...
3. Prove or disprove: For integers a and b, if a|b, then a^2|b^2. 4. Suppose that for sets A,B,C, and D,A∩B⊆C∩D and A⊆C\D. Prove that A and B are disjoint.
Prove this statement. Z[i] is the Gaussian integers: Let α ∈ Z[i]. Then α is a...
Prove this statement. Z[i] is the Gaussian integers: Let α ∈ Z[i]. Then α is a unit if and only if N(α) = 1.
3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g...
3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g : N→Z defined by g(k) = k/2 for even k and g(k) = −(k + 1)/2 for odd k. Prove that g is a bijection. (a) Prove that g is a function. (b) Prove that g is an injection . (c) Prove that g is a surjection.
Prove that the poset (Z+, |) (i.e., the positive integers ordered by divisibility) is a distributive...
Prove that the poset (Z+, |) (i.e., the positive integers ordered by divisibility) is a distributive lattice.
Prove by contradiction that: For all integers a and b, if a is even and b...
Prove by contradiction that: For all integers a and b, if a is even and b is odd, then 4 does not divide (a^2+ 2b^2).
Show that there are infinitely many pairs integers a and b with gcd(a, b) = 5...
Show that there are infinitely many pairs integers a and b with gcd(a, b) = 5 and a + b = 65
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT