composite. 10. Suppose that n = 2³ × 5² × 7 × 17³. Give the prime factorization of n² and nº (Hint: Do not work too hard.)

Q: d) How many 4 digit numbers can you make from the elements of A without repetition contain the…

A: We shall solve first question only as per answering guidelines. If you want others to be solved…

Q: 6. Find the value for n for the regular heptagon.

A:

Q: 10 use n= n1c 16 +hlk-1 + h 16 +no pug of Rul e cf divisibility for 7 16,21

A: we have, n=nk10k+nk-110k-1+....+n1(10)1+n0 Let n=nk10k+nk-110k-1+....+n110+n0=7k for some integer k.…

Q: 21. Given that "( = "('3, the value of the integer n is 6 D 3

A: To find the value of n in the given problem, we use the definition of binomial coefficients.

Q: How many digits does a number 8^(n). 5^(3n+4)  have, if n belongs to N ?

A: Given data Number: 8n .5 (3n+4) We have to find digits in number.

Q: Justify whether it is true to say that the given is the nth term of an AP  1+n+n2

A: We have to say that whether the given nth term is in A.P. where, 1+n+n2 We have given nth term of…

Q: 8) The number 4050 can be factored into prime divisors as: 2 x 3 x 3 x 3 x 3 x 5 x 5 a) Determine…

A: We have to solve

Q: 12 Find the term of (a – 3b)" that has b in it.

A:

Q: - Moores Sth Grade ELA/Witing x 2 zearn x + 1107 M4|L7 Tape Fractions - of a number is 18. What is…

A: We have to find number

Q: 3. Select the D from the given options so statement becomes true and write that in the (1) If the :…

A: Part 1 When N÷5 the remainder can be any number from 0 to 4 Now, for the remainder to be equal to 1,…

Q: Show that if 5 divides n2 with remainder 4, 5 divides 3n3 with remainder 2.

A: Given that 5 divides n2 5 n25 n×n5 n5 n3 As it gives the remainder 4 on dividing by 5. Therefore it…

Q: 2. Determine the highest power of 5 that divides each of the following positive integers. a) 112,250…

A:

Q: 5n. Determine for which n n-2 For nz 2, let on =

A: Here we have to determine the n for which |an|<1 for all n≥2 where an=5nn2-2

Q: If n is a natural number, the number 34n+4 – 43n+3 is divisible by: -

A: Given : To find : A positive number which can divide above expression

Q: 11. When the marchers in the annual Mathematics Department Parade lined up 4 abreast, there was 1…

A: let the number of Persons in department be x. according to the given Problem, x≡1(mod 4)x≡2(mod…

Q: ( 4 25 77 ) ind the cholesky factorization A=GG¹

A: Matrix is positive definite. So cholesky factorisation is possible.

Q: (b) If n > 4 is composite, then n divides (n – 1)!. -

A: Question 6) (b) We have to show that if n>4 is composite, then n divides (n-1)!

Q: nth term of an AP  1+n+n2

A:

Q: Q4: Consider the 5-digit can be formed using the digits 0-9 mbers, with distinct digits (no…

A:

Q: (b) An integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

A:

Q: 11. What do you obtain when you raise 27 to the 8/3 power ? * 1/3 of (27 to the 8th power)

A: Any number a can be written as , where b is any natural number. Also, 27 is a cube of 3, so 27 can…

Q: Suppose that n=24.35.112.133. How many divisors does n have?

A: Given,  n = 24 35 112 133 Then (4+1)(5+1)(2+1)(3+1) = 5×6×3×4=360 It has 360 number of divisors

Q: Suppose m = apɑp-1*** a2ɑ1ao and n = bpbp-1*…* b½b¡bo are two numbers with the same digits so that n…

A: 7) a. Given that ai=bj. Without loss of generality assume that i>j. Now the value of the digit ai…

Q: If x is the greatest prime factor of 39 and y is the greatest prime factor of 72, what is the value…

A:

Q: (b) Give two different interpretations of the bino- mial coefficient (") for non-negative integers n…

A: First we will give two different interpretations of the binomial coefficient nk for non-negative…

Q: A box with a square base and no top is to be made from a square piece of cardboard by cutting 2 in.…

A: Let consider that x be the length of one side of the cardboard When 2 inches are removed from each…

Q: 2. What is the prime factorization of 15x y? O 3.5 2y O 3.5 x y Y O 15 - x * y Y 3-5 22 y y

A:

Q: For which values of n does n! have n or fewer digits

A: Solution is as follows

Q: Choose the prime factorization of 12 O 2.3 10 O 23.3.5 o 10 12 O2.5.12

A: to find prime factorization  Start by dividing the number by the first prime number 2 and continue…

Q: O Find the elements of [9]=,-

A: We need to find the elements of 9≡4 . That is we need to find the set of all integers which are…

Q: 1. Show that b, = (n!)'/n > 20.

A: Consider n!1n=an1n.

Q: 2. A toy company sells 3-packs of sphere-shaped bouncy balls. If the company ships the three bouncy…

A: Finding the empty space in the given figure.

Q: (c) Show that for 2" > 4n for n ≥ 5.

A:

Q: Al. a. Find an integer that leaves a remainder of 2 when divided by either 3 or 5, but that is…

A:

Q: Each of following has 9 as a factor except: A) 18,018 B) 18,081 C) 81,180 D) 81,181

A: A) 18,018 B) 18,081 C) 81,180 D) 81,181To find which of the following does not have 9 as a factor

Q: . How many four-digit numbers are there with different digits and simultaneously: (a) divisible by…

A: Given: Total number of digits = 10 (0 to 9) Number of digits in a number = 4

Q: 44. The number n can be expressed as the product of four prime numbers, exactly three of which are…

A: Concept:

Q: 6. If x is any positive integer, which one of the following terms could be added to the sum of 2x +…

A:

Q: Question Which of the following is the least common multiple LCM) of 2-3-13 and 2-3 m 02¹-3¹-13²…

A:

Q: If n is 0 what is 8n

A:

Q: 5 2. (-3-2)

A:

Q: (a) At a glance, determine the digit d so that 64,275,67d is divisible by 4. Is there more than one…

A:

Q: 4. Explain why the following statements are true or False. (a) There is an even number that is a…

A:

Q: 3. If BC = x-11, AC = 7x-36, and AB = 3x + 14, find the following.

A:

Q: 58. The integer k is the product of four different prime numbers. If k divided by 22 is a multiple…

A:

Q: If n is 10 what is 8n

A: Given that n is 10. Then what is 8n.

Q: (c) For each integer n, if n is odd, then 8 divides (n4 + 4n² + 11).

A:

Q: ove that n’ +5n is divisible by 6 for all n E N.

A:

Q: 4. Give the other possible appropriate names for 2. M

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