rainbowowlkitte rainbowowlkitte

13-10-2019
Mathematics

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Solve the polynomial congruence x² ≡ 1(mod3).

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sqdancefan sqdancefan

13-10-2019

Answer:

x is any integer not a multiple of 3

Step-by-step explanation:

This is equivalent to ...

(x mod 3)² = 1

x mod 3 = ±1 . . . . . . taking the square root

Possible values of x mod 3 are 0, 1, 2 (≅-1), so the only value excluded is 0.

x mod 3 ≠ 0 . . . . . . for any integer x

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