2-) Find all in tegers x such thet 5x = 12 (mod 7) 10x = 4 (mod 1) 7x E 16 (mod 10d ond 1occ < x < 3000

Q: let x  be a fixed but arbitrary integer. Do there exist infinity many integer y such that,…

A: Let x = x0 be fixed given integer. Then,

Q: Let p, q, and r be real numbers such that p + q +r = 26 and '/p + lq + '/, = 31. What is the value…

A:

Q: Find all natural numbers in such that n²<z". Prove your assertion.

A:

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to find the negation of the given statement. In logic, the negation…

Q: Kample tetx be Let X€2Z. Prove that for cveri integer n2 , x^is cuen × is aven 2.

A: Yes, for n greater than or equal 2(n is a positive integer) if x is even then x^n will also be even.…

Q: 6) If X is N(45,5) for i = 1, 2,..., 25; find: 25 (a) P (30 < (X-45) < 55) 221 b) P(30< (X -45) 2 <…

A: The objective of the question is to find the probability of two different scenarios for a normally…

Q: Prove that for a # -1, a>0,n EN IS (1+a)^ n >=1+na.

A: Here let A=(1+a)n, a≠-1, a&gt;0, n∈N and B=1+na

Q: Let a,n∈N. Assume that n≥2. Show that if a^(1/n) is rational, then it is an integer.

A: The detailed solution is as follows below:

Q: 3. Find the following: A. 3^0 mod 5 1 B. 3^1 mod 5 3 C. 3^2 mod 5 1 D. 3^3 mod 5 4

A:

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: -1 1 x+1 coth - In X = 2 x-1

A: We have to prove coth-1x=12lnx+1x-1

Q: * Determine wether each one of lie followeng is a decryption function of f(x) = 5x +2 (mod 26) Prove…

A: To check if it is a decryption function we can calculate the function for each alphabet and see if…

Q: Prae that x4 -5x +3 is ineducible ouer Q

A: Given polynomial is f(x)= x^4 -5x^3 +3

Q: 2. Encrypt the message STOP POLLUTION by translat- ing the letters into numbers, applying the given…

A: let's encrypt the message "STOP POLLUTION" using the given encryption functions one by one.For the…

Q: Let F(n) denote the Fibonacci numbers. Prove the following property for n ≥ 3 directly from the…

A:

Q: Find all integers x (if there exist any at all) such that x^2 + 5x + 6 is prime. Justify that your…

A: We have to find all integers x (if there exist any at all) such that x^2 + 5x + 6 is prime.

Q: Fibonacci numbers are defined as f₁ = 1, f₂ = 1 and fn = fn−1 + fn-2, n ≥ 3. Show that f< (5/3)".

A:

Q: 21. How many positive integers x are there such that 3x has 3 digits and 4x has four digits?

A:

Q: List all numbers x such that 0≤x<100 and x ≡ [3,1] mod [4,5]

A: Given,           0≤x&lt;100, and  x ≡ [3,1] mod [4,5].

Q: Show that the set A = {n^2/ (n+1): ne N} is unbounded in R.

A: To prove that the set A={n2n+1:n∈N} is unbounded in R,

Q: Prove that xk = x* mod |G| for x € G for any integer k.

A: Prove it considering two cases.

Q: Prove that 3! 2(n+3) = n r=0 (-1) n "Cr r+3 Cr

A:

Q: If a and b are integers with gcd(a, b) = d Then gcd (-- d.

A: Given a statement

Q: . show that for every positive integer n, if n^2+2 is prime then n is a multuple of 3. Is the…

A:

Q: n —(2) - (-) (1)¹(1)(). (n-1)

A:

Q: 2. Find the largest negative x € Z that simultancously satisfies 4x = 9 (mod 5) 2x = 0 (mod 6) x =0…

A: Given : 4x = 9 (mod 5) 2x = 0 (mod 6) x = 0 (mod 4)

Q: 2 + х2 — 1 х — 1 х+1 5х 1

A:

Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

A:

Q: 1- 9/if it of Prove that yś(-)- TT

A: In the question it is asked to prove y'(0)=π for the given function y=2xcos-1(2x)-1-4x2.

Q: is the following fucntion analytic in mod(z)&lt;2 and/or mod(z)&gt;2. sqrt(z^(2)+2z+2)/ z^(2)-4z+3

A: The objective of the question is to determine whether the given function is analytic in the regions…

Q: 10. By Binomial Theorem (2a – b)* =16a* – 32a’b+24a*b? – 8ab³ +b* | a. TRUE. b. FALSE.

A: We know the binomial therom expansion

Q: Find a such that 5= 7* modulo 13.

A: Given: 5≡7xmodulo13. The objective is to find the value of x.

Q: Need help with True or False for the following... (I will put what I believe As (T) or (F)) 1. For…

A: Let's evaluate the provided statements and their negations as well as the converses and…

Q: Let A = {4n^2 + 1 | n ∈ Z}. Show that the size of A is equal to the size of Z≥0. Z≥0 is the set of…

A: A set A is said to be countable  if there is a bijective map between A and set of natural numbers .…

Q: why/where/how does the 1 and the 0 about from at the end of the last few steps?

A: By Leibniz rule for differentiation under integration sign is given by, Here we need to…

Q: Compute 7^35 (mod 3) ..

A: As per our guidelines, we are supposed to solve only first subpart. Kindly repost other subpart as a…

Q: 9) If X-N(68,7.29), then p(X < 65) =

A: normal distribution  x~N(68,7.29)

Q: (п-1)! d) DE (x"-1nx)

A:

Q: Work the modular arithmetic problem. (12 9)(mod 3). (12 9)(mod 3) =(mod 3)

A: The given modular arithmetic problem is -  (12·9)(mod 3) We have to solve the above problem.

Q: Find the smallest value of n such that f(x) is O(x^n) for each of the following. d) lnx…

A:

Q: Find all solutions of the congruence x^2 = 208 (mod 7368787).

A: As per the question we are given the following quadratic congruence equation : x2 ≡ 208 (mod…

Q: let f(r) = r – r' +x +x? – 1 and q = 41 Find f(x)-1 (mod q) Show all step. The answer should be…

A: Solution

Q: 4. (**) Let [x] be the greatest integer that is ≤r. Then prove (10) IN [(k,n)

A: The idea of the problem is to use the definition of the greatest integer function.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.