Compute the residue of a = = 230 18 = 1073741806 = {0x3FFFFFEE} over the following...

 

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Compute the residue of a = = 230 18 = 1073741806 = {0x3FFFFFEE} over the following numbers using the method you learned in class. Show your work. Then verify your results using SageMath. Show all results in Hexadecimal. (a) P₁ = 2¹7 - 1= {0x1FFFF} (Mersenne prime) (b) p2 = 226. -5= {0x3FFFFFB} (Pseudo-mersenne prime) (c) b = 216 = {0x10000} (Not a prime number) Compute the residue of a = = 230 18 = 1073741806 = {0x3FFFFFEE} over the following numbers using the method you learned in class. Show your work. Then verify your results using SageMath. Show all results in Hexadecimal. (a) P₁ = 2¹7 - 1= {0x1FFFF} (Mersenne prime) (b) p2 = 226. -5= {0x3FFFFFB} (Pseudo-mersenne prime) (c) b = 216 = {0x10000} (Not a prime number)