Show directly that for p a prime integer, p can be written as p=(a)^2 - d(b)^2 then d is a perfect square in Z/pZ. Hint: Are a and b elements of Z/pZ?    Are a and b elements of Z/pZ*?

Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

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Q: Determine a conclusion. Choose the correct answer below. the null hypothesis. There is difference…

A: That is, there is no evidence to conclude that there is significant difference between the two…

Q: (1) As usual, let (a, b) stand for the Greatest Common Divisor of a and b. Is it true that k(a, b) =…

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Q: Let ß = (1,3,5,7,9,8,6)(2,4,10). What is the smallest positive integern for which ßn = ß-5?

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Q: 2. Factor x from ax + bx

A: We have to factor x from ax+bx.

Q: If d is a positive and not perfect square integer in [6,8]. Assume that √d = [ao; a₁, a₂, 3, 1, a5]

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Q: Write the following in stan 7x² +4x³ +5+2x

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