Draw the Hasse diagram of all positive divisors of p³q*.

Q: Find the number of elements in the conjugacy class of (abc)(def) in S₆

A: We have to find the number of elements in the conjugacy class of (a b c)(d e f) in S₆

Q: Find a zero divisor in Z2021- Prove that if n is composite, then Z, has divisors of zero.

A: Consider the provided question,  Need to prove that if n is composite , than ℤn has divisors of…

Q: Prove that the product of any k consecutive positive integers is an integer multiple of k!.

A:

Q: 2. U={x|x is an integer, 2<x<10}. A and B are subsets of U such that A= {multiples of 3}, B={factors…

A: Using set theory we have to answer following.

Q: Prove that the order of 3 modulo 19 is a divisor of 18.

A:

Q: Determine all integers n &gt; 1 for which (n-1)! is a zero-divisor in Zn.

A: Given: Zn. To Do:We have to determine all integers n&gt;1 for which n-1! is a zero divisor in Zn.

Q: What are the two things we need to show to prove that need to show to prove that is a binary…

A: To find: the conditions such that "*" is a binary operation or binary composition.

Q: Prove that for any integer n, we have n - 2 is not divisible by 4.

A:

Q: 4. Show that for all positive integers n, n! + 1 has a prime divisor greater than n.

A: Let n be an integer such that n&gt;1. All prime divisors of n!+1 must be bigger than n. This is…

Q: Is this a binary operation on the set of all positive integers? r*s = qt where q and t are both…

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Q: The coefficient of x³ in (1 + x² + x² + x6)4 is determined by the 4-tuples o integers (a1, a2, a3,…

A:

Q: nsist only of of even length. Generalize to find the EGF number of ations that consist only of…

A: To find: (1) The EGF for the number of permutations that consist only of cycles of even length.…

Q: List all common divisors of each of the following pairs of integers 24, 32

A: Given(24,32)To list common divisors of above

Q: 8) Prove that n³ + 2n is divisible by 3 for any natural n. 5

A:

Q: If gcd(7, a) = 1, prove that either a +1 or a – 1 is divisible by 7. 20

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Q: A binary string is a word containing only Os and 1s. In a binary string, a 1-run is a non-extendable…

A: def count_1_runs(n): binary_representation = bin(n)[2:] # get the binary representation of n…

Q: How many elements are there in the greatest conjugacy class of 5 ?S

A:

Q: 3. We say that an integer c is a common divisor of integers a and b if cla and cb. We say c is the…

A:

Q: (a) Show that the set Rof all multiples of 3 is a subring of 7. (b) Let k be a fixed integer. Show…

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Q: 3. Suppose b > 1 is an integer. The proof of the existence of a base b representation of any integer…

A: (a)

Q: Complete the table of values below.

A:

Q: Show that among any 4 n−1 people, there are either some n of them who mutually know each other, or…

A: Pigeonhole Principle  :  Simple form Theorem 1  :  If n + 1 objects are put into n boxes, then at…

Q: prove that n²_1 is divisible by when ever n is odd an Positive integer.

A:

Q: Find all divisors of 20.

A: The given number is .The aim is to find the divisors of .

Q: Evaluate L{3e cos 10r cos 41. S+1 s+1 A. 2 (s+1) +16 (s+1) +100 S-1 S-1 B. 2 (s-1) +16 (s – 1) + 100…

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Q: 10. Prove that n³-n is divisible by 6 for every integer n.

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Q: Let m and n are relatively prime, positive integers. What is the greatest common divisor of 5m + 7m…

A: Since m and n are relatively prime, we can use the following property: For any two relatively prime…

Q: Let x Є Z. Prove that if x2 - 8x + 11 is divisible by 4, the x6-1 is also divisible by 4.

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Q: Prove: Any positive integer can be represented as an aggregate of different powers of 3, the terms…

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Q: Show what the divisors of 120 are and what they add up to.

A: Divisors of 120=1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120