[C] Perform the modular arithmetic. 1. (9 + 15) mod 7 2. (5 + 22) mod 8 3. (42 + 35) mod 3

Q: Number theory

A: Here, x6+1 is reducible in the field mod 2 (when x = 1). So,  the reduction of  x6+1 will be either…

Q: solve 6メミ q modis

A:

Q: (a) 55 mod 7. (b) –101 div 3.

A: (a) 55 mod 7  As 55 = 7•7+6 So that  55 mod 7 = 6 mod 7

Q: Identify the real number subset(s) that each of the following belong in. Pleasegive all…

A: Given query  Need to identify the numbers .

Q: (a) Find two integers satisfying the equation r³ + 24x² – 2 = 0 mod 23.

A:

Q: Use the diagram below to find the two angles. Be sure to show all of your work. axt15 3XF1O 3x+10

A: From the diagram we know that (2x+15)+(3x+10) = 180. So,             (2x+15)+(3x+10) = 180…

Q: True or False?  −29≡5(mod 17)

A:

Q: Solve each equation for x. (If there is no solution, enter NO SOLUTION.) (a)     x + 8 ≡ 1, (mod 9)…

A: We solve each equation for x.

Q: Number theory

A:

Q: onsider the theorem: “for any integer x, if x mod 6 = 5, then (x2-2x+4) mod 4 = 3.” (a) Give an…

A: We recall some definition regarding modulo arithmetic and solve this problem. The detailed steps are…

Q: The remainder when aa is divided by 77 is 22 and the remainder when bb is divided by 77 is 55. (So a…

A: Given:          a≡2 mod(7)  and b≡5 mod(7)

Q: The binary number of 371 is a. 1011110011 b. 101111011 c. 101010011 d. 101110011 O b a d.

A:

Q: Using appropriate methods, reduce (i) 419 mod 47, (ii) 141-10156 mod 47, (iii) 483 mod 47, (iv) (419…

A: We have to reduce the following congruent equation.

Q: Evaluate the expressions. (a) 50 div 7 7.143 (b) 50 mod 7 1 ]x

A: We shall answer the following in next step. We also recall the definitions