Show that 2047 is a strong pseudoprime to the base 2 by showing that it passes Miller’s test to the base 2, but is composite.

Q: For which odd primes p is 3 a square mod p?

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Q: Any number n is congruent to the sum of its digits modulo 4. Select one: True False

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Q: . Show that 1729 is a Carmichael number.

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Q: ct enumeration, find the period of the following congruential generator: Xi+1=11Xi mod 32, given…

A: Given, the congruential generator is :Xi+1 = 11Xi mod 32, Also, given X0 = 1 We see that the…

Q: Use Eulers thm to find , 7଼8003 mod 1000

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Q: Give an odd prime p congruent to ±1 modulo 12. Show that (3) = 1.

A: Please see the attachment

Q: The ISBN-10 0-669-03925-4 is the result of a transposition of twoadjacent digits not involving the…

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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: Books are identified by an International Standard Book Number (ISBN), a 10-digit code x1x2... x10,…

A: Let us start finding q and m values

Q: How to find 85307 (mod 739)?

A: To make it simple , divide power by 4 then solve .

Q: For which odd primes p is 5 a square mod p?

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Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?.

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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: The inverse of 7 modulo 26 is 15

A: Given a statement

Q: Find the least residue of 448 modulo 7

A: Given problem is : Find the least residue of 448 modulo 7

Q: What is the least residue of 7162 modulo 17?

A: Multiplication rule for congruencesIf a ≡ b (mod n) and c ≡ d (mod n), thenac ≡ bd (mod n). Power…

Q: For which odd primes p is 5 a square modulo p?

A: As we know that  a is Quadratic residue mod p if and only if   a(p-1) /2 =1 mod p . If p and q are…

Q: Show that if p is an odd prime, then n = 2º – 1 passes Miller's test base 2 -

A: Given that n=2p-1 where, pis odd prime. Since, 2p is an even integer. Then, n=2p-1 is an odd…

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

A: We know that 2 is even prime. And all other primes are odd.

Q: Prove: The nth Fibonacci number Fn is even if and only if 3 | n.

A: The nth Fibonacci number Fn is even if and only if 3|n.

Q: The prime number 8191 is a None Mersenne primте тmber Carmichael umber Inverse of 7 modulo 11

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Q: What sequence of pseudorandom numbers is generated using the pure multiplicative generator xn+1 =…

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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: Do all four problems. 1. Prove that there exists a unique prime number of the form n2 – 4, where n…

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Q: 122 is congruent to 5 modulo17 ?

A: To check whether -122 is congruent to 5 modulo 17 or not

Q: 1. Solve the congruence 17x ≡ 42 (mod 100). 2.Compute the remainder of 3293 when divided by 97…

A: 1) solve the congruence 17x=42+100k implies17≡42+100k as we know gcd17,100=1 and 1/42 now, using…

Q: Find oll integers Such thot 24! x =1 Cmod 2) 5x = 3. (mod 8) and 1500 < X <2000

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Q: To Determine the value that 46 is congruent to IN modulo 7

A: Note that, If a and b are integers and n &gt; 0, then a ≡ b (mod n) to mean n|(b − a) and It can be…

Q: Suppose Alice and Bob have the same RSA modulus n and suppose that their encryption exponents eд and…

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Q: Books are identified by an International Standard Book Number (ISBN), a 10-digit code x1x2... x10,…

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Q: Find all prie 8. If p > q 2 5 and p and q are both primes, prove that 24 p2-q?.

A: Given: p≥q≥5 and p and q are both primes

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?

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Q: 2. For which odd primes p is 11 a

A: If p is a prime, then by Fermat's Little Theorem

Q: Show that 1729 is a Carmichael number.

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Q: Prove that 2^(27) - 1 is not a prime number.

A: A prime number is a natural number greater than 1 that is not a product of two smaller natural…

Q: State Fermat's Little Theorem. In the groun (7/1017)x find 5100 5101 and 5202 (101 is a prime…

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Q: Suppose b is any integer. If b mod 12 = 7, what is 6b mod 12? In other words, if division of b by 12…

A: To determine the value of 6b mod(12) if b mod(12) = 7.

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: A sequence of pseudorandom numbers is generated as follows Xo = 4 x₁ = ( 6x₁-1 + 5 ) mod 13 if i > 0…

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Q: Show that in Zm there is no nilpotent element except 0 by letting m be the product of three distant…

A: Statement : In Zm, there is no nilpotent element except 0 We need to prove the  above statement by…

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: Calculate 433940584939 mod 988027. Show how do obtain your claimed solution.

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Q: If n and a are prime to 7 then prove that nº – a® divisible by 7?

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Q: If a (mod 0) = a, How would you interpret the congruence a ≡ b (mod 0)?

A: According to the given information, it is given that:

Q: Every prime number is odd. True False

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Q: Use the repeated squaring method to calculate the following: 16^10 (mod 230)

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Q: Solve for a a ≡ 13 mod 5353

A: To solve  a ≡ 13 mod 5353

Q: 8. Primes (a) Prove there are infinitely many primes

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 8) 91 is a pseudoprime to the base

A: 8) 91 is a base pseudoprime to the base .....

Q: use the "successive squaring" method to check 'by hand and modest calculator' that a^48610 == 1 (mod…

A: Fermat's little theorem says, If n is a prime number, and a is not divisible by n, thenan-1≡1mod n.…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.