Show that x^8 ≡ 2 ( mod 13) has no solutions.

Expert Solution

Colby Messinger answered 2 years ago

Determine the solution of the following equation mod N. 1.7x≡2 mod 15, where N= 15 2.x≡8...

Determine the solution of the following equation mod N. 1.7x≡2 mod 15, where N= 15 2.x≡8 mod 11, x≡3 mod 19, where N= 209 3.x≡2 mod 7, x≡2 mod 11, x≡1 mod 13, where= 1001

let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod...

let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod p), i.e., the number of elements (x,y), x,y=0,1,...,p-1, which satisfy x^2 - 2 y^2=1 (mod p)

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19)

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19) 2. Fine the subgroup of Z24 (the operation is addition) generates by the element 20. 3. Find the order of the element 5 in (z/7z)

Find all x ∈ Z such that x≡2 mod 221 and x≡5 mod 184.

Compute the following: (a) 13^2018 (mod 12) (b) 8^11111 (mod 9) (c) 7^256 (mod 11) (d)...

Compute the following: (a) 13^2018 (mod 12) (b) 8^11111 (mod 9) (c) 7^256 (mod 11) (d) 3^160 (mod 23)

Solve the following system of congruences: x ≡ 2 (mod 14) x ≡ 16 (mod 21)...

Solve the following system of congruences: x ≡ 2 (mod 14) x ≡ 16 (mod 21) x ≡ 10 (mod 30)

a) Use Fermat’s little theorem to compute 52003 mod 7, 52003 mod 11, and 52003 mod 13.

a) Use Fermat’s little theorem to compute 52003 mod 7,52003 mod 11, and 52003 mod 13. b) Use your results from part (a) and the Chinese remaindertheorem to find 52003 mod 1001. (Note that1001 = 7 ⋅ 11 ⋅ 13.)

Let x, y ∈ Z. Prove that x ≡ y + 1 (mod 2) if and...

Let x, y ∈ Z. Prove that x ≡ y + 1 (mod 2) if and only if x ≡ y + 1 (mod 4) or x ≡ y + 3 (mod 4)

0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod...

0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod 5, 5 mod 7〉 24 mod 35 = 〈4 mod 5, 3 mod 7〉 1 mod 35 = 〈1 mod 5, 1 mod 7〉 13 mod 35 = 〈3 mod 5, 6 mod 7〉 25 mod 35 = 〈0 mod 5, 4 mod 7〉 2 mod 35 = 〈2 mod 5, 2 mod 7〉 14 mod 35 = 〈4 mod 5, 0 mod 7〉...

Show that f(x) = x^4+x^3+3x^2+7x−8 is irreducible over Z.

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