Question

Solve the following equations using step-by-step equational reasoning, and list each step. a) Solve the following...

Solve the following equations using step-by-step equational reasoning, and list each step.

a) Solve the following equation for x ∈ ℤ/43ℤ: x2 ≡ 25 (mod 43)

b) Solve the following equation for x ∈ ℤ/19ℤ: x2 ≡ 5 (mod 19)

c) Solve the following equation for x ∈ ℤ/55ℤ: x2 ≡ 1 (mod 55)

d) Solve the following equation for x ∈ ℤ/41ℤ: 3 * x2 ≡ 7 (mod 41)

e) Solve the following equation for x ∈ ℤ/49ℤ: x2 ≡ 8 (mod 49)

f) Solve the following equation for x ∈ ℤ/21ℤ: (8 * x2 ) + 4 ≡ 6 (mod 21)

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