For which primes p > 7 is 7 a square mod p? Your answer should be of the form p = {a1, a2,... , a} mod n, where a; E {1, .,n - 1} for all i= 1,..., k. mod

Q: For inputs of 0 and 1 and mod 2 arithmetic describe the output ofthe formula z + xy + xz in the form…

A: As per the question we have to describe the output of the formula : z + xy + xz For the inputs of 0…

Q: 4. For any integer n, show that if n³ = 1 (mod 47), then n = 1 (mod 47).

A: To show that if n3≡1(mod47), then n≡1(mod47), it can use proof by contradiction.Assume that…

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: If x = 2 (mod 5) and y = 4 (mod 5) then 2x – 3y =? (mod 5)

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Q: Find the smallest positive integer for which x mod 3 = 2 and a mod 4 = 3 What is the next smallest…

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Q: 3. 78 + x = 3 ( mod 5) 4. 89 = (x + 3) ( mod 4)

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Q: Using Euler's Theorem, simplify the following numbers: o = 3, q = 5, x = 2, and a = 2. Which of the…

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Q: If n| m and a = b(mod m), then a = b(mod n).

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Q: Which of the following are true modulo 12? (1) Does 5z = 6 mod 12 have a solution? How many? (2)…

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Q: Does 5x = 6 mod 12 have a solution? How many?

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

Q: In the following question: " Let a, b ∈ Z. Show that if a ≡ 5 (mod 6) and b ≡ 3 (mod 4), then 4a +…

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Q: 35. Let p be an odd prime number. Prove the following statements. (a) (7) = 1 if and only if p = 1,…

A: We have to prove given statement if p is an odd number.

Q: 4. Consider the following statement: For all n N and x = Z, x² = 1 mod n Which of "if", "only if",…

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Q: The natural numbers are N= {1,2,3,..}. The prime numbers are P = {2,3,5,7...}. True or false? ØSN…

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Q: Find the integer a such that a. a = -43 (mod23) and -22 ≤ a ≤ 0.

A: Find the integer  such that  and .

Statements and Logic

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