Determine the length of the period for the decimal expansion of 8881 Note that 8881 83 107. =

Q: Find g.c.f. and l.c.m. of the numbers 2730 and 693. SHOW YOUR WORK! Are the numbers 2730 and 693…

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Q: 15-Find the 13th term of an AP in which a = 7, and d = 6: The correct answer is (85) Select one:…

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Q: explain with detail Mersenne primes

A: Prime numbers are natural numbers that are divisible by only 1 and the number itself. In other…

Q: Prove 10^47+67 is not a prime(use Fermat's). Thank you :)

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Q: prove the formula of Mersenne primes

A: A number of the form is a Mersenne prime if and only if p is prime.To prove this we need to show…

Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: Find the prime factorization of 793169. To show your work you must use Theorem 2

A: Consider the equation

Q: What is the greatest prime you must consider to test whether 5317 is prime? The greatest prime to…

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Q: Find n, if the ratio of the fifth term form the beginning to the 1 +$3) 43 fifth term from the end…

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Q: For the first 5 odd primes, show that Wilsn's theorem holds to be true.

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Q: Use the Fundamental Theorem of Arithmetic to prove that the 7th root of 12 is irrational.

A: Given : Fundamental Theorem of Arithmetic . To show: 127 is irrational .

Q: 259 ompute the Legendre symbole (3), noting that 733 is prime.

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Q: Using Fermat's Little Theorem find 52003 mod 455. Note that 455 is not a prime number and 455…

A: We are asked to use Fermat's Little theorem to find 52003 mod455. Fermat's Little Theorem states…

Q: Show that every nonzero residue (mod 17) can be written as a power of 3

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Q: 2. Is 1501 a square modulo the prime number 3739? Explain.

A: Step 1: Step 2: Step 3: Step 4:

Q: (a) Show that, for any odd prime p > 5, 1 if p = 1, –5 (mod 12) (주) -1 if p= -1,5 (mod 12)

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Q: Prove: If the sum of the digits of a number in base bis divisible by b 1, so is the number.

A: Given statement: Sum of digits of any number (x) in any base b is divisible by b-1. To prove: The…

Q: Fermat's theorem is not true for some prime number. Select one: O True O False

A: Fermat's theorem states that if p is a odd prime number, then for any integer a, the number ap − a…

Q: Find 1112 mod 13.

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Q: Find the prime factorization of 224331. List the product of primes in increasing order (in the form…

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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: Use the pigeonhole principle to prove that the decimal expansion of a rational number min eventually…

A: To Prove:  Using the pigeonhole principle that the Decimal expansion of a rational number m/n…

Q: give examples how to find mersenne primes

A: a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime…

Q: Q15. What is the first (rightmost) digit in the base 3 expansion of the base 10 number71?

A: Given: 15. A base 10 number 71. To find: The first(rightmost) digit in the base 3 expansion of given…

Q: Every even integer greater than 2 is sum of two primes? Give your views on this?

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Q: There are Infinitely many Primes.

A: To prove that there are infinitely many Primes.

Q: Solve by mathematical induction For all integersn> 3, 4(4" – 16) 4 + 4* +4 + .. ……+4" =

A: Solution: The objective is to prove that the given statement using mathematical induction.

Q: Find all the primes less than 50 with primitive root 3.

A: A primitive root modulo a prime number is an integer such that every non-zero integer less than…

Q: For integer values of a, use a proof by contraposition (also called contrapositive or indirect…

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Q: TRUE or FALSE: 1. There is no integer n such that 4 | (n^2-2) 2. The GCD of all prime numbers is 1.…

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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: The binary expansion 0.abcd... means 23 24 and each binary digit a, b, c, d, ... is either 0 or 1.…

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Q: If in the expansion of (1 + n}+", the 5th term is 24 times the 3rd term, fnd the value of n.

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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: Is 0.101001000100001000001… a repeating decimal? Is it rational or irrational? Explain (hint if the…

A: Explained below