Use modular arithmetic and three prime values m, m2, and m3 to verify that 7425 * 625 = 4640625 %3D

Q: Write a prime number and a composite number, both under 100, that are relatively prime.

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Q: Use mathematical induction to show that 5? − 1 is divisible by 4. Determine the starting value as…

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Q: 31x = 14(mod127) 26x = 3(mod97)| 3(mod97) 17x = 87(mod101) 24x = 591(mod1001)

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Q: If 6 decimal digits only are allowed, then the chopped representation of the number 0.123456789 is…

A: Here the number is given as 0.123456789 We need till 6 decimal places If the 7th decimal place is…

Q: How many integers from 1000 through 9999 must you pick in order to be sure that at least two of them…

A: As per our guidelines we are supposed to answer only? One question ( if there are multiple questions…

Q: DOference of twin primes is not divisible by 2. :Select one True False

A: We Know that Two prime numbers are called twin primes if there is present only one composite number…

Q: ) Find an integer having the remainders 3, 11, 15 when divided by 10, 13, 17, respec- tively.…

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Q: List five different natural numbers that are congruent to 8 modulo 6.

A: # as per the guidelines we are entitled to solve one question at a time ,please resubmit the other…

Q: rd. 17. Show that every decimal palindromic integer with an even number of digits is divisible by…

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Q: Find the Prime Factorization of 648, 1056, and 1496. Provide at least one divisibility test for each…

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Q: Use the Mathematical induction to verify that , for n any positive integer, 6" – 1 is divisible by 5

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Show by induction that if (n) is a positive integer, then ((n^3) - n) is divisible by 6.

A: Given statement is

Q: 17. Prove that n is square - free every prime number to sat:sfies does not divide ).

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Q: 1 101101, and 101, 2. 10111102 and 102 and 112 3. 1000012

A: Since there are multiple questions the first question is answered as per our guidelines. Kindly…

Q: Find all prime numbers between 130 and 230.  Show using the Seive of Eratosthenes.  Show table.

A: Let us make a grid that has numbers from 130 to 230 130 131 132 133 134 135 136 137 138 139 140…

Q: 11. What is the smallest prime divisor of 52020

A: We first find unit digit of Given number then use divisiblity test.

Q: IS 971 a prime! Why? How about 5183?

A: To determine whether 977 ia a prime number.Also to check whether 5183 ia a prime number.

Q: Find the sum of all positive odd integers from 1 to 1239: 1+3+5+7+...+ 1239.

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Q: 16. Devise a way of checking whether or not a number is divisible by 24. Test your method on 36 and…

A: 16

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: Find the remainder of 1111^2222+2222^3333+3333^4444+4444^5555 modulo 17

A: We have to find the remainder of 11112222+22223333+33334444+4444555517 Firstly we take 1111222217 if…

Q: PRODD 2 Determine whether the integer 701 is divisors. Do the same for the integer 1 Sieve of

A: Theorem for prime numbers: A number p is called prime number if there exist a number p0 such that,…

Q: (1) The integer 123 is a prime.

A: (1) Given, the integer 123 is a prime.

Q: Use mathematical induction to prove that any amount of postage that is an integer amount greater…

A: We have to prove that any amount of postage that is an integer amount greater than 53 cents can be…

Q: Show that the number 7,176,825,942,116,027,211 is divisible by 9but not divisible by 11.

A: Given: Number  7,176,825,942,116,027,211  To check: Given number is divisible by 9 but not divisible…

Q: 2. An integern is divisible by 3 if and only if the sum of its digits is divisible by 3. (Hint: Use…

A: We will prove the given statement.

Q: Find the product whit base of eight 5eight × 7364eight

A: Procedure: 1. Convert the given number into decimal numbers. 2. Multiply the numbers.  3. Convert…

Q: If n is prime, then 2" – 1 is prime.

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Q: Which positive integer less than 21 are relatively prime to 21? 18 O 19 O 21 O 24 O

A: Which positive interger is less than 21 is relatively prime to 21?

Q: 9. Evaluate 1110 0101 0111 1101 and interpret the result as the binary (base two) representation of…

A: Answer:-  First we have to understand ("^") what this symbol represent , so basically it represents…

Q: noosing a positive integer from 100 to 999, what is the poSSibility of choosing a positive integer…

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Q: Find an integer between 100 and 150 divisible by 9.   How do i figure this out, I am completely…

A: A number is divisible by 9 if the sum of the digits is divisible by 9.

Q: Represent each of the following numbers as normalizedbase 2 floating-point numbers using 4digits to…

A: Given, the number is 3/8, we have to represent the number as normalised base 2 floating-point number…

Q: is 539 prime, composite, or neither? explain in a few words how you know.

A: It is a composite number.

Q: How many distinct rearrangements of the letters in millenia are there? Give your answer as an…

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Q: The different permutations of the word MATHEMATICS is 4989600 Select one: O True False

A: As per our answering guide lines we are allowed to solve only first complete question. Kindly repost…

Q: Find 53745 mod 64719 N 53 2809 39744 Clear my choice

A: To find 5339745mod 64719. Let us use Chinese remainder theorem to evaluate this.  Now,…

Q: Number theory

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Q: Use modular arithmetic to prove that, if n is an integer not divisible by 5, then n^4 − 1 is…

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Q: Show that the principle of mathematical induction implies that I is the leact p natural number.

A: Solution of the problem as follows

Q: How many 6 digit numbers are divisible by 5? Assume repetition is allowed. 12000 180000 60000 200000

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Q: Is 7, 8, 9, 11 are pairwise relatively prime. صواب ihi

A: Two nos. a and b are said to be relatively prime iff gcd(a,b)=1

Q: find the sum of all integers between 300 and 800 that are exactly divisible by 14

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Q: Use Modular Arithmetic to evaluate 26x350166 (mod 4). Show your steps.

A: Solution

Q: a. What is the 21st digit in the decimal expansion of b. What is the 5280th digit in the decimal…

A: Define a general formula for each digit position and use the general formula to calculate the digit…

Q: what is the nunber 1'7 Composite number Neither Prime nor Composite Prime number

A: If a and b are two distinct prime numbers then, a highest common factor of a and b is, 1

Q: 18. Show that every base 7 palindromic integer with an even number of digits is divisible by 8. 19 D

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Q: ime? W

A: Introduction: A number is prime factorised or integer factorised when it is broken down into a set…

Q: 27-8^n a prime? Why?

A: answer is in next step

Q: 2. Use mathematical inc positive integer n.

A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.