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valkas [14]
2 years ago
9

Solve the polynomial congruence x² ≡ 1(mod3).

Mathematics
1 answer:
igor_vitrenko [27]2 years ago
3 0

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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