how that in the domain of integers of the form a+bsqrt(-17) the factorization 169=13*13=(4+3sqrt(-17))(4-3sqrt(-17)) demonstrates that unique factorization into primes fails in that domai

Q: Compute A - 613 and (613)A, where A = - A-613 = ☐ 6 - 4 3 2 -7 - 3 1 3

A:

Q: (1) What is gcd(31212021 + 3, 31212021 - 3)? I am aware of 3121 is a prime number, and 2021 is…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Is it true that (3 x EN) (x²-3x +20 is a prime)? O True False

A: Is it true that ( there exists x in N)(x^2-3x+20  is a prime ) ?   True False

Q: Use Wilson's Theorem to verify that 4(29!) + 5! is divisible by 31.

A: The given number is 4 (29)! + 5! . Our aim is to verify that the given number is divisible by 31…

Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

A: Number System

Q: If n is a positive integer prove that 3^(2n) - 26n -1 is divisible by 676

A: if n is a postive integer prove that 3^(2n) - 26n -1 is divisible  by 676

Q: A) (1 + √₂)² B) (1 -√2)² c)(1+√2)(1+√-2) D)(1+√2)(1-√√2) E)√2² + (√2)² Which of the above…

A: A) 1+22B) 1-22C) 1+21+2D) 1+21-2E) 22+22

Q: can someone help me with Finding the prime factorizaton of 245

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Q: (d) (11 × 14" + 1) is a composite integer for every positive integer

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Q: Prove or disprove: There exists an integer a such that 14 | (3a – 5) and 21 | (2a +3).

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Q: (g) 111... 111 (126 ones) (2) Prove that the numbers given in each part cannot be prime…

A:

Q: Solve for X, show all calculation in binary number system only X = ((1110)₂-(0011)₂) (10011010)₂)…

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Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

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Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's Theorem: If p is a prime and a is a positive integer and not divisible by the prime p, then…

Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's states that if p is a prime and a is a positive integer not divisible by p, than ap-1≡1 mod…

Q: 28000 +38000 + 48000 + 58000 + 68000 Prove that 1 8000 is a multiple of 13 using Fermat's Little…

A: Given that                                 we have to prove that it is multiple of 13 by using…

Q: While proving (a*2(2a+1 is an integer for the case a = 6q +1 which of the following will be obtained…

A: We are given with a(a+1)(2a+1)6 We need to substitute a=6q+1

Q: √38 10 V √ 65

A: To check whether the given triangle is right triangle or not.

Q: prove the difference of the squares of two z integers is always divisible by 16 (i.e. z1^2 - z2^2 =…

A: We prove that (z_1)^2-(z_2)^2=16k for some integer k, then we say that divisible by 16.

Q: 3 Show thet x+3x+2 has four in 76 zenos.

A:

Q: What is the coefficent of 5 in (x + 1)7 - x²(x+3) 5

A:

Q: 11. (a) Give the prime factorizations of both 144 and 1200. (b) Use your answers from part (a) to…

A:

Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

A:

Q: Is it true that GCD(6,14,119) x LCM(6,143,119)= 6x143x119?

A: We know that GCD(a,b,c) × LCM(a,b,c) = axbxc