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

Q: Determine:-a. gcd(2,10) lcm(2,10)b. gcd(20,8) lcm(20,8)c. gcd(12,40) lcm(12,40)d. gcd(21,50)…

A:

Q: 21. Find two different factorizations of the number 21 into primes of the form a + b v-2, where a…

A:

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: [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: 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: Factor 8051 into its 2 prime factors.

A: To find the 2 prime factors of 8051

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: Let p > 5 be the prime number. Prove that the expression p – 10p +9 is divisible by 1920.

A: We have to prove that the expression p4-10p2+9 is divisible by 1920.

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

A:

Q: If a, b are two distinct prime number than a highest common factor of a, b is: (2 ab

A: HCF of two numbers is found out by taking common prime factors from both the numbers the…

Q: Prove that 5 does not divide 5n+3 for any integer n.

A:

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: If p + 2 is a prime number, prove that p² + 3 is divisible by 4.

A:

Q: p + 2 is a prime number, prove that p2+3 is divisible by 4. (2.5

A: Prime and divisibility

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: The prime factorization of 1001 is @113.13 3.11.13 7,11.13 3.11.13

A:

Q: 5. Let n be a positive integer and p1,P2,P3, . „Pn be n distinct primes. If m is a positive integer…

A:

Q: Show that if m is a positive integer, then p(m²) = m· ¢(m). Hint: consider the prime factorization…

A: Introduction: The phi function of Euler denoted by ϕ is one of the most important number-theoretic…

Q: Suppose a, b are relatively prime integers. (a) Show that gcd(8a, 8b) = 8. (b) Show that d = gcd(a +…

A: We will use the fact that if a,b are relatively prime integers, then : gcd(a, b) = 1

Q: If p is a prime number greater than 3, which of the following represents the sum of the positive…

A: we will check all the options to ensure which is correct.

Q: If n = p,P2 ... P where the p, are distinct prime numbers, how many ways can n be written as a…

A: First let us formulate the problem in a different way. Look! we have to find the total number of…

Q: 10. If a, b and p are positive integers, what is the LCM of ap, bp^3 and a^2p^2? 1 a^2bp^3 abp p^2

A: Since the student has mentioned to solve multiple questions (no. 10-12), but we can solve one…

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: If a, b,n are integers and a^2 + b^2 = n, then the remainder of n upon division by 4 is not 3.

A: Here a and b are two integer then n is the sum of two square. There is only one case n to be prime…

Q: 3. The GCF of any two distinct prime numbers is 1. (Distinct they are not the same number) means

A:

Q: of its prime factors. 2. 24

A:

Q: Find all prie 8. If p > q 2 5 and p and q are both primes, prove that 24 p2-q?.

A: Given: p≥q≥5 and p and q are both primes

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: What is the coefficient of p5q5 in the expansion of (p+q)10?

A:

Q: If n = 4k + 3, does 8 divide n2 - 1? (Assume that n and k represent integers.) O Yes, because n2 - 1…

A:

Q: А. If p 2q 5 is a prime number, prove that p2-q? is divisible by 3.

A:

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: If m is a positive integer, does 6 divide (2m)(m+2)(3m+3)? True False

A: Here, the given number is: (2m)(m+2)(3m+3)=2(m(m+2))3(m+1)=6m(m+1)(m+2) because multiplication is…

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 if 2n−1 is prime then n is prime.

A: We have to show that if 2n-1 is prime then n is prime.

Q: Let p, q, and r be primes other than 3. Show that 3 divides p2 +q2 + r2.

A:

Q: What are the 5a + 20a - 60 factors of O 5 (x-6)(x+2) • 5 (x+6)(x-2) O 5 (x-6)(x-2)

A:

Q: Choose the prime factorization of 120. O 22.3.10 O 23.3.5 o 10 12 O 2.5 12

A:

Q: Find the negation of the following statement: "Every non-zero integer can be factored as a product…

A: We have to find the negative of the statement "Every non-zero integer can be factored as a product…

Q: Find the GCD and LCM of the 2 214 and 25 125 using prime factorization

A: GCD=3 LCM=18542250

Q: Let p > 5 be the prime number. Prove that the expression p* - 10p? + 9 is divisible by 1920.

A:

Q: Let p and q be odd primes and let m and n be positive integers. Explain why U(p") O U(q") is not…

A: given, let p and q be odd primes. and n be a positive integer.

Q: What is the coefficient of æ10 in (æ + 3)13?

A:

Q: List all the factors of 99. 1, 3, and 9 3, 9, 11, and 33 O1,9, 11, and 99 O1, 3, 9, 11, 33, and 99

A:

Q: Show that if a and b are relatively prime then (a+2b,2a+b)=1 or 3.

A:

Q: Let p, q, and r be primes other than 3. Show that 3 divides p2 + q2 + r2.

A: We have to prove that 3 divides p2+q2+r2, where p,q and r primes other than 3.

Q: 4. Find them if: (a) lcm of two consecutive positive integers is 812; (b) lcm of twin primes is 899.

A:

Q: Let M= (1 x 2 x 3 x 4 x ... × 1000) + 1 What can you say about the prime factors of M? Why?

A: M= (1 x 2 x 3 x 4 x ... × 1000) + 1 Prime factor of this number is the number itself, there is no…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.