Let t= 20389208 mod 4 and M= t+25 a. Find integers a and b such that...

Let t= 20389208 mod 4 and M= t+25

a. Find integers a and b such that 0<a<M, 0<b<M and ab= 0 (mod M)

b. Find integers a and b such that 0<a<M, 0<b<M and ab= 1 (mod M)

Thank you in advance!

Expert Solution

Thank you ??

Colby Messinger answered 1 year ago

Give an example of integers a, b, m such that a 2 ≡ b 2 (mod...

Give an example of integers a, b, m such that a 2 ≡ b 2 (mod m), but a 6≡ b (mod m)

Show that if a and b are integers with a ≡ b (mod p) for every...

Show that if a and b are integers with a ≡ b (mod p) for every prime p, then it must be that a = b

S = Z (integers), R = {(a,b) : a = b mod 5}. Is this relation...

S = Z (integers), R = {(a,b) : a = b mod 5}. Is this relation an equivalence relation on S? S = Z (integers), R = {(a,b) : a = b mod 3}. Is this relation an equivalence relation on S? If so, what are the equivalence classes?

Q−3: [5×4 marks] a. Find a, b if a+2b=107 mod 9 and 2a+b=-55 mod 7. b....

Q−3: [5×4 marks] a. Find a, b if a+2b=107 mod 9 and 2a+b=-55 mod 7. b. Write the prime factorization of 229320 and 49140, hence find GCD and LCM. c. Convert the following number (1303)4 to base 5. d. Using the Prime Factorization technique determine whether 173 is a prime. e. Use the cipher: f(x)=(x+7) mod 26 to decrypt “THAO ALZA”.

3. (4 marks) Let a and b be positive integers. Is gcd(5a + b, 11a +...

3. Let a and b be positive integers. Is gcd(5a + b, 11a + 2b) = gcd(2a + b, 3a + 2b)? If yes provide a proof. If not, provide a counterexample.

Prove the following. Let T denote the integers divisible by three. Find a bijection f :...

Prove the following. Let T denote the integers divisible by three. Find a bijection f : Z→T (Z denotes all integers).

Let {W(t),t≥0} be a standard Brownian motion and let M(t)=max0≤s≤tW(s). Find P(M(9)≥3).

Let S=$32, K=$33, r=4%, σ=25%, δ=0, T=0.5 year, and n=2. a.) Find u and d. b.)...

Let S=$32, K=$33, r=4%, σ=25%, δ=0, T=0.5 year, and n=2. a.) Find u and d. b.) Use the risk neutral probability to find the price of a European put c.) Use the risk neutral probability to find the price of an American put.

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and...

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and B at the point corresponding to ? = 1. (b) Find the equation of the osculating plane at the point corresponding to ? = 1. (c) Find the equation of the normal plane at the point corresponding to ? = 1

a.) Prove the following: Lemma. Let a and b be integers. If both a and b...

a.) Prove the following: Lemma. Let a and b be integers. If both a and b have the form 4k+1 (where k is an integer), then ab also has the form 4k+1. b.)The lemma from part a generalizes two products of integers of the form 4k+1. State and prove the generalized lemma. c.) Prove that any natural number of the form 4k+3 has a prime factor of the form 4k+3.

Question