Compute the prime factorization of: gcd(1200725694, 7260624) 12007256942.36.77 7260624 24 33.75 T Ex: 2^3* 3

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: 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: Which among the following is a rational number? (A) (B) 3.1425547.... (C) 32 (D) 36

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Q: Use casting out nines to see if these calculations may have an error. If incorrect, give the correct…

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Q: 7. The heights reached by 15 model rockets launched by the students in Mr. Fiori's science class are…

A: The main objective of this question is, by using the stem leaf plot we need to provide minimum and…

Q: Show that 7 divides (1111)³³³³ + (3333)¹¹¹¹

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Q: How many 3 digit even numbers can be created if repetition of digits is allowed

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Q: Express 0.112112112... as a fraction of integers.

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Q: Use the the Binomial Theorem to calculate 11^11 (just giving the end result is not enough.)

A: To find the value of 1111 using the binomial theorem. Now, the Binomial expansion of (1+x)n is:…

Q: Find the order of 5 modulo 2^100.

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Q: If x^677 ≡ 3 mod 2020, find x.

A: We have   x677≡3mod2020⇒x677-3=2020m   where m is integer different values of m we get different…

Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

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Q: Use the Fermat's Theorem to determine the last digit of 12347865435 when divided by 11

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Q: ou are told that 159238479574729 = 529

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Q: Compute the prime factorization of:                     gcd(75, 90)                     75 = 3 · 52…

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Q: value of (p tq +r)¶? the three smallest primes, what is the 8. If p, q, and r are, in increasing (A)…

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Q: Consider a product of an odd prime with itself and represent it as a sum of two squares. 1. 13^2 =…

A: According to question given:Product of an odd prime with itself and represent it as a sum of Two…

Q: Find 21234567 (mod 509822653

A: The objective is to evaluate 21234567mod 509822653. Obtain the prime factorization of 509822653. The…

Q: Determine the least residue of 56^1010 (mod 323).

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Q: The prime factorization of 7007 is B.11.13 O11.13 V.11.13 011³.13

A: First option is correct.

Q: Find the least residue of  -5 -46 modulo 14.

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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: 7 relatively prime uct and quotient of a

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Q: bers {1, 3, 6, …}

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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: 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: Find a primitive root modulo 2 * 19^2022

A: Consider the number n=2×192022. We know that a primitive root of modulo n is an integer g such that…

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: Compute phi(6^2 x 4^3). (Note that this is not a prime power factorization.)

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Q: Calculate 2^1212 (mod 9211), reducing it to a positive number less than 9211. Show your…

A: We have to find out remainder when Noted that Since So to get the required result ,we have to find…

Q: how to calculate 250 to 260 binominal dictribution

A: p=0.95Now, n=250, p=0.95, q=0.05

Q: We are given the continued fraction expansion for the square root of 89: [9; 2, 3, 3, 2, 18, 2, 3,…

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Q: Compute the prime factorization of:         gcd(699840, 1215000)            699840 = 26 · 37 · 5…

A: We have to find the prime factorization of gcd of two given numbers.