Show that {Z5, +5,×5} is a field.

Show that a6-1 is divisible by 168 whenever (a, 42)=1.

Subtract the following two polynomials and express your answer in simplest form. (12p2 15p + 3)- (2p2 17p- 2) D) 10p4 - 2p2 , 5 A) 10p2. 2p - 5 Óption 4 Option 1 B) 10p2- 2p 5 C) 10p2 - 2p 1 O Option 2 Option 3

Express x8 - x as a product of irreducibles over Z2. Please be clear, correct and legible. Thank you.

Suppose that 2^n − 1 is prime. Show that n must also be prime. (Hint: try to find a convenient factorization of the polynomial x^n − 1 if n is composite).

D) 3x-32x-3 Which polynomial is in standard form? A) 6d +2d-d + 4 B) 4d + 6d+5d- 1 -d+ 2d+6d + 2 Dj 7d-3d 6d-4 dete ncethedome of the funcion

write a polynomial in expanded form that has zeroes -5, 0, and 2/5

Find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer.

Divide the polynomial -5x^2-2+3x+2x^4 +4x^3 by 2x-3+x^2, and check the result 2) Divide the polynomial -x^3+9x+6x^4 -x^2 -3,by 1+3x and check the result 3) Divide the polynomial 3x^3-16x^2-27 by x-6, and check the result 4) Divide the polynomial-3x^2-x^3+5 by x-4, and check the result

a. Without tables, show that -(p v (-p ^g)) a nd -p ^-q are logically equivalent.