Make sure that all your answers are explained carefully. (a) Remember that the order k = ordma is the smallest positive integer for which ak 1 mod m. Determine the order of 11 modulo 21. (b) For each of the following positive integers, say whether it has a primitive root or not. Explain why. (i) a = 19, (ii) b = 250, (iii) d = 45.

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Q: Which irrational number can be multiplied by: 41 to get a product that equals 1 41 O -41

A: We can find the answer as below

Q: QUESTION 1 Find an integer x between 220 and 260 that satisfies x = 39^123 (mod 41). Your answer…

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A: To find The order of the integer 4 modulo 19.

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A: In the given problem we have to find the multiplicative inverse mod 26 for α = 19. Show all steps.

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A: given a≡2(mod113),b=5(mod113)a3≡23(mod113)a3b≡235(mod113)56b≡280(mod113)56b≡54(mod113)155≡15mod113)

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A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

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Q: Then Find inverse of 21 mod 200.

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Q: Then Find inverse of 21 mod 200.

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