Prove: in L number psiz 12, for every prime poiz, [p] = [1], [5) , [7) , or [11]

Q: Prove that Va - Vb is irrational number if 'a' and 'b’ are prime number?

A: Given To prove that a-b is irrational number if a and b are prime number.

Q: Q2: Find the Eulerian Circuit in the following weighted graph starting at the vertex 'a'

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Q: Suppose that the number 'a' has a property that for every natural number n, a ≤ 1/n. Prove that a ≤…

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Q: Let x be an integer. Prove that, if x mod 9 = 5, then 9|(x^2-2x+3)

A: Given: x mod 9=5 then, 9|x2-2x+3|

Q: Assume an unlimited supply of coins worth 5 cents and 9 cents. Prove that some

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Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

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Q: 5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following…

A: The objective of this question is to find the number of positive integers between 1 and 99 that are…

Q: Prove that for all integers a, b, and c if a divides b then for all naturla numbers n a^n divides…

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Q: If fN is the set of the first 100 positive integers, A is the set of odd numbers between 50 and 90,…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Prove that, all integers x and y, x^2-4y≠2  1a. Prove that all numbers of the form 1007, 10017,…

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Q: Prove that Leonardo's congruous numbers are always divisible by 24.

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Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: Prove that for any 9 consecutive natural numbers, there exists one number that is prime to the other…

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Q: 5) Let n be a positive integer such that 7 | (8-1). Prove that 7 | (8=*1 - 1). (Hint: Rewrite 8*1…

A: Given: Let n be a positive integer such that 78n-1. To prove: 78n+1-1

Q: Prove that among 7 positive integers, there are always two integers such that either their sun or…

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Q: Prove that 6">5" + 9 for any integer n ≥ 2.

A: Mathematical induction is a technique used to prove statements about well-ordered sets of natural…

Q: Show that 2 + V5 is imational number

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Q: One of the striking properties of Fibonacci numbers is that gcd(Fm, Fn) = Fd, (*) where d = gcd (m,…

A: 1. We see,        F9 = 34    [Fibonacci series : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,. . . . . ]…

Q: Let 2k +1 be a prime number. Prove that then k = 0 or k = 2" for some n > 0. %3D

A: Solution:- Let 2k+1 be a prime number k=0 or k=2n for some n≥0   For, k=0 2k+1=20+1 2k+1=1+1…

Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

Q: S²₁ Sinmxsinhxbx = 2 x if m=n So min

A: To prove:- ∫-ππsinmxsinnxdx=0if m≠nπif m=n

Q: Let {\mathcal S}S be the set of all (nonnegative) 4-digit integers. How many integers does {…

A: Here given S is set of all (nonnegative) 4-digit integers We have to calculate,  How many 4 digits…

Q: Please provide justified answer asap:::: Show that n is odd if and only if n^2+4n+1 is even.

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Q: Show that Consider the Fibonacci numbers {F} defined by F₁ = 1, F₂ = 1, and Fn+2= Fn+1 + Fn. - Fn =…

A: Introduction: In mathematics, a recurrence relation is a significant connection that expresses the…

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

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

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}

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Q: ) How many,8-distinct/digit numbers can be formed if the numbers áre amultiple of/5 and contain the…

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Q: Prove that 2 divides a if and only if 2 divides ao. Prove that 4 divides a if and only if 4 divides…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: 4. For natural numbers n and k, prove (C) - ()

A: We have to prove

Q: Since the next prime after 7 is​ 11, the smallest composite number whose prime factors are all…

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Q: Prove that tim 51

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: What is the smallest positive integer x in the equarion: 1=3x+2(mod 7)?

A: We have to solve the equation 1 = 3x + 2 (mod 7)⇒1 - 2 - 3x = 0 (mod 7)⇒-1 - 3x = 0 (mod 7)⇒3x = - 1…