Problem 6.2 Find the prime factorization of 10!.

Q: If x is any positive integer , then the sum of 6x and 11x is always divisible by what?

A: x is a positive integer. Find sum of 6x and 11x is divisible by what?

Q: 2. What are the greatest common divisors of these pairs of integers? (a) 37 x 5 x 7,21 x 3 x 5°

A:

Q: (6.1) Prove if r is a positive, even integer then 10* – 1 is divisible by 11. (6.2) Prove if r is a…

A:

Q: 21 divides 4(n+1) + 5(2n-1) whenever n is a positive integer.

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: (7) Recall that vp(n) denotes the highest power of the prime p that divides the nonzero integer n.…

A: Given that denotes the highest power of the prime p that divides the nonzero integer n.First we have…

Q: d) How many non-negative integer solutions are there to the following problem? I1 + x2 + I3 = 10…

A: The problems related to calculating the number of ways can be solved using the combinations. The…

Q: Find the fourth term m the papansion of

A: 1-23x36 use the binomial theorem a+bn=∑i=0nnian-ibi 1-2x336=∑i=066i· 16-i-2x33i

Q: (d) (11 × 14" + 1) is a composite integer for every positive integer

A:

Q: Find (characterize) all primes p > 3 that satisfy (금) 1.

A:

Q: Find a formula for the general term a, {5, 8, 11, 14, 17, .} 5n + 3 On+3 O 3n + 2 O 2n + 3

A: We can answer the question as below

Q: I also found that the expression was divisible by 13 at n=6 and n=10. Is there anyway you could…

A: Any number n can be written in the form          n = 3m, or 3m+1, or 3m + 2 for some integer m.…

Q: 3. Find the greatest common divisor and least common multiple of a = 2338712132 and b = 365511²13.

A: a = 2338712132    = 233850712110132 b = 365511213    = 20365570112131

Q: Show that the sum of the squares of the first n natural numbers is given by,S=(n(n+1)(2n+1))/6

A: We have to show that the sum of the squares of the first n natural numbers is given by S=nn+12n+16…

Q: 2. Factor x from ax + bx

A: We have to factor x from ax+bx.

Q: True or False. Briefly explain If p is odd prime then p divides 2p−1+(p−1)!.

A: Given: is an odd primeTo check:The prime divides  or not.Results used:Wilson's Theorem:For any…

Q: #5 Find An if n is a positive integer and A = 4 -3 - 2

A:

Q: 8. Find lcm(143, 227), lcm(306, 657), and lcm(272, 1479). 9 Prove that the greatest common divisor…

A: Here is solution of only question no 8.

Q: Let p and q be prime numbers. (1) If p is not equal to q, how many generators does Zpq have? (2) If…

A: Given p and q be primes.

Q: Expand the following binomial powers.

A: Note : As per the authoring guidelines, when there are multiple subparts are posted in a single…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.