9. Which of the following prime numbers is not a factor of the integer 330? (1) 11 (3) 3 (2) 7 (4) 5

Q: The number of factors of prime numbers are None of the mentioned O 30 Depends on the prime number

A: No. Of factor of prime no. Means how many divisor consist of a prime no.

Q: Determine whether it is possible to express 1 as a liner combination of 1 = m· 44 + n· 91 ,. for…

A:

Q: How many positive integers less than 10000 are there which contain at least one 7 or at least one 9…

A:

Q: [The answers to the following two subquestions(a and b) are INTEGERS.Put ONLY the integer in the…

A: Given the expansion  a 2z3-3z9b y+z5+y-z5

Q: !. 2. Find 100 irrational nember s between o andd 3. Find 50 rational numbers betwee and 2. 4. Fmd…

A: We know  2<e<3 So,   0<e1000<1100      as  e<3<10 So, 0<e103<1100 Define ,…

Q: The number of factors of prime numbers are Depends on the prime number 3 O None of the mentioned O

A: Prime numbers are the numbers which have only two factors one factor is 1 and other factor is 2

Q: 19. What is the value of (pk) when p is prime and k is a positive integer?

A: We know that the value of the Euler ϕ-function at the positive integer n is defined to be the number…

Q: The number of factors of prime numbers are Depends on the prime number None of the mentioned (3 2

A: Given query to find number of factors of a prime number.

Q: 4) Prove that the product of any three consecutive integers is divisible by 6.

A: We have to show that product of any three consecutive integers is divisible by 6

Q: R.1. Show that among 14 distinct integers, there must be two that have the same remainder when…

A: In order to prove this statement pigeonhole principle has to be applied. According to pigeonhole…

Q: Find L{(3th+1 – 2)*}. O 9(2n+1)! 4 | s2n+2 O 9(2n+2)! 12(n+1)! - 82n+3 sn+2 9(2n+2)! 2n+3 O…

A: L3tn+1-22

Q: . Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when…

A: Consider an integer x that has a remainder of 2 when it is divided by 5 Thus x=2 mod 5 0r x=5k+2 It…

Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

A:

Q: 2. Find the missing numbers in the magic square below. 2 13 10 11 6. 12 15 1 4-

A: Consider the provided table,

Q: The number of factors of prime numberss are (None of the mentioned Depends on the prime number (2 (3

A: Prime number is only divisible by 1 and that number itself

Q: What is an integer between 2.3 and 3.3

A: We have to find an integer which is greater than 2.3 and less than 3.3

Q: W found that 2,3,5,7 and 11 are not factors of 211. Can we conclude that 211 is prime? Why or why…

A: To check whether 211 is prime number on not.

Q: What is the smallest positive integer that has 6, 8, and 10 as factors?

A:

Q: . Which of the following prime numbers is not a factor of the integer 330? (1) 11 (3) 3 (2) 7 (4) 5…

A:

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: Show by mathematical l Induction y 4n-2 3. +17 can be divided by +22 possitive integers 16 far all

A: To prove the given statement by using mathematical induction.

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

A:

Q: 1. What are the possible remainders of prime numbers greater than 2 when it is divided by 7? а. 1,…

A:

Q: How many integers 2 ≤ n ≤ 65 have no prime divisor less than or equal to ¹/³?

A:

Q: 4) Find the number of positive integers not exceeding 1,000 that are not divisible by 3, 5, or 11.

A:

Q: Show that for all integers m and n, if the remainder is 2 when m is divided by 4 and the remainder…

A: we have to Show that for all integers m and n, if the remainder is 2 when m is divided by 4 and the…

Q: 4. Find all the prime numbers that can be expressed in the form n2 – 9 for some integer n.

A:

Q: 5. How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

A:

Q: 6.) Find the sum of the first 50 positive integers ending in 6.

A:

Q: 9. Find the sum of all'integers between 90 and 190 if each integer Is divisible by 17 (Hint. The…

A:

Q: 2. Classify as integer or non-integer. • 28 • -58 • 7/16 • 7/21 • 21/7

A:

Q: What is the coefficient of z12 in (6-12z)12 O a. P(12,6)* -612 O b. C(12,0)* -(1212) O . 1212 O d.…

A:

Q: 5. Use the direct proof to show that " If n is an odd integer, then n2 + 3 is even

A:

Q: Q7. How many positive integers not exceeding 100 are divisible either by 6 or by 10?

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Prove that 4 divides 6 7" - 2.3" for all integers n 20.

A: We need to prove that 4 divides 6.7n-2.3n for all integers n≥0.

Q: Show that (n + 1)! > 2"+3, for n > 5.

A:

Q: 5. Find the number of positive integers less than 700 that are divisible by 3 but not divisible by…

A:

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: Show that n! > 3 for n ≥ 7

A: We have to prove this assertion that, n! > 3  for n≥7 We will prove this statement by the method…

Q: (6) Find the sum of the integers for 7 to 508 Tmelusive,

A: first term (a0) = 7last term( an) = 508,     d = 1 ( natural no.)first we have to find total no of…

Q: 3. The v77 is between what two integers?

A:

Q: Show that the sum of twin primes p and p + 2 is divisible by 12, provided that p> 3.

A: Let p, p + 2 be twin primes. Then p *(p+1) + 1 = p^2 + 2p + 1 = (p+1)^2 ,  a perfect square.

Q: 8. Show that no prime number of the form 4k +3 can divide a number of the form n2 + 1.

A:

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

A:

Q: Suppose A = {2, 5, 7, 9, 13, 25, 26}. (a) Find n(A).

A:

Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

A:

Q: 4. The area of a parallelogram is 198 square units. If the base and the height of the parallelogram…

A:

Q: The number of factors of prime numbers are Depends on the prime number 3 0 2 0 None of the mentioned…

A: The number of factors of a prime number is 1 and prime itself. So there are 2 factors of prime…

Q: 1.What is the smallest number that can be exactly divided by 2, 3, 4, 5  and 8 ? 2.What are the…

A: To answer the given questions.