Question

If g(x) = x + x^2, prove that g(n) − 4g(m) = 0 has no solutions...

If g(x) = x + x^2, prove that g(n) − 4g(m) = 0 has no solutions for positive integers m and n.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove by induction that 2 x 1! + 5 x 2! + 10 x 3! +...+...
Prove by induction that 2 x 1! + 5 x 2! + 10 x 3! +...+ (n2 + 1) n! = n (n + 1)! For all positive integers n
Prove the following statements: 1- If m and n are relatively prime, then for any x...
Prove the following statements: 1- If m and n are relatively prime, then for any x belongs, Z there are integers a; b such that x = am + bn 2- For every n belongs N, the number (n^3 + 2) is not divisible by 4.
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.
Prove that if x ∈ Zn − {0} and x has no common divisor with n...
Prove that if x ∈ Zn − {0} and x has no common divisor with n greater than 1, then x has a multiplicative inverse in (Zn − {0}, ·n). State the theorem about Euler’s φ function and show why this fact implies it.
Using induction prove that for all positive integers n, n^2−n is even.
Using induction prove that for all positive integers n, n^2−n is even.
Prove that for all positive integers n, (1^3) + (2^3) + ... + (n^3) = (1+2+...+n)^2
Prove that for all positive integers n, (1^3) + (2^3) + ... + (n^3) = (1+2+...+n)^2
Prove that the complete set of solutions to the congruence x 4 − x 2 +...
Prove that the complete set of solutions to the congruence x 4 − x 2 + x + 3 ≡ 0 (mod 51) is given by {x ∈ Z: x ≡ 36 (mod 51)}
Prove: If f(x) = anx^n + an−1x^n−1 + ··· + a1x + a0 has integer coefficients...
Prove: If f(x) = anx^n + an−1x^n−1 + ··· + a1x + a0 has integer coefficients with an ? 0 ? a0 and there are relatively prime integers p, q ∈ Z with f ? p ? = 0, then p | a0 and q | an . [Hint: Clear denominators.]
Let a1, a2, ..., an be distinct n (≥ 2) integers. Consider the polynomial f(x) =...
Let a1, a2, ..., an be distinct n (≥ 2) integers. Consider the polynomial f(x) = (x−a1)(x−a2)···(x−an)−1 in Q[x] (1) Prove that if then f(x) = g(x)h(x) for some g(x), h(x) ∈ Z[x], g(ai) + h(ai) = 0 for all i = 1, 2, ..., n (2) Prove that f(x) is irreducible over Q
Show 2 different solutions to the task. Prove that for every integer n (...-3, -2, -1,...
Show 2 different solutions to the task. Prove that for every integer n (...-3, -2, -1, 0, 1, 2, 3, 4...), the expression n2 + n will always be even.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT