Question

Compute x, such that 10⁴≡x ( mod 19).


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Answer 1

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Question:

Compute x, such that 10⁴≡x ( mod 19).

Solution:

10² = 100≡5 (mod 19)

10⁴ = (10²)² ≡ 5² (mod 19)

10⁴ ≡ 25 (mod 19)

10⁴ ≡ 6 (mod 19) that is (25≡6 (mod 19))

Therefore x = 6.

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NOTE:

• While solving congruent equations, we get infinitely many solutions compared to finite number of solutions in solving a polynomial equation in Algebra.