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

Q: Let x and y be positive integers such that the prime factorization of x has exactly five 3's and the…

A: x = 35×k          k is an integery = 33×l           l is an integer

Q: Determine whether there are infinitely many primes that have a remainder of 12 when divided by 25.…

A: Given question is Determine whether there are infinitely many primes that have a remainder of 12…

Q: 16 Jlgu The Greatest Common Divisor of two prime numbers a and bis

A: Greatest Common Divisor: The greatest common divisor (GCD) of two or more integers is the largest…

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: 2. Find six rational numbers between 3 and 4

A: We can solve the given problem using concept of rational numbers which is, Therefore d=(y-x)/(n+1)…

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: Find the greatest natural number n such that n + 10 divides nº + 100.

A:

Q: If a and b are two distinct prime numbers, then the greatest common divisor of a and b is O ab

A:

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: 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: 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: 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: Suppose that the prime factorizations of two positive integers x and y are expressed using a common…

A: The prime factorization is breaking down a number into the product of only prime numbers. These…

Q: The integers 77 and 105 are relatively prime.

A: Relatively Prime integers: Two integers mand n are called relatively prime if gcd(m,n)=1. Given two…

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: 1) What is the different between prime and composite number? 2) For any integer a, show that…

A: 1. A prime number is a positive integer whose only divisors are 1 and the number itself. A composite…

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: .If p 5 is an odd prime, prove that either p? – 1 or p² + 1 is divisible by 10.

A:

Q: The integers 77 and 105 are relatively prime. صواب İhi

A: By finding the factors of given numbers you can find the solution :

Q: Do you thinkthat there are infinitely many primes of the n -1

A: there are infinitely many primes of the n -1 Explain the above statement

Q: There exist two prime numbers and such that their product gives 1261

A: We have to find two prime numbers whose product gives the required number

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

A:

Q: Q2: Use Fermat's method to analyze the number into its * prime factors (1745)

A:

Q: Before arriving at his famous conjecture, Goldbach had conjectured that every odd positive integer…

A: Goldbach conjecture says that every integer greater than 5 is the sum of three primes.

Q: A. If p 2q25 is a prime number, prove that p-q is divisible by 3.

A:

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: The number of primes of the form n² – 6n + 5 where n is an integer is O 2 O 3 O 1

A: We have n2 -6n+5 ⇒n2-5n-n+5⇒n(n-5)-(n-5)⇒(n-1)(n-5)

Q: Let n be any integer. If n=3k+5 for some integer k. Does 91 6n-3 No, because 6n-3= 18k+30-3 which is…

A:

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: Do you think it is worthwhile, or useful, to solve the puzzles proposed in Euclid's theorem of…

A: The objective is to solve the puzzles proposed in Euclid's theorem of primes There are infinitely…

Q: 3. Given that n is a positive integer, prove by induction that, the 7"+ 5 is divisible by 6. Guess a…

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

Q: Find the canonical prime factorization of the following using Fermat's Method and solve for the…

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: Q2: Use Fermat's method to analyze the number into its prime factors (1745)

A: We have to find prime factorisation of 1745 using Fermat's method.

Q: Give an example of a prime p of each of the forms: (a) 4k +1 (b) 4k + 3 (c) 6k + 1 (d) 6k + 5.

A: Que Ans -  prime number - A number Is divisible only by itself and number 1 is called prime number…

Q: 5. Invent a positive integer a that has at least 8 decimal digits and a ones digit of 7. Estimate…

A:

Q: prove that it is not possible to find four distinct prime numbers p, q, r, s such that ps − qr = 0.

A:

Q: Given that 7,999,999,999 has at most two prime factors, find its largest prime factor.

A: 7,999,999,999 has at most two prime factors, We have to find its largest prime factor.

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: If n is an even integer, then 3n° is an even integer.

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: (1). Prove that adding an irrational number with a rational number is an irrational number, and show…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

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…

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…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.