Mathematics · Number Theory

Let p be an odd prime such that p &equiv; 2 (mod 3). Let &mathbb{F} p be the field with p elements. Consider the subset E of &mathbb{F} p × &mathbb{F} p given by: E = {(x, y) ∈ &mathbb{F} p × &mathbb{F} p : y 2 = x 3 + 1}. Which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

E has exactly p elements

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Let p be an odd prime such that p &equiv; 2 (mod 3). Let &mathbb{F} p be the field with p elements. Consider the subset E of &mathbb{F} p &times; &mathbb{F} p given by: E = {(x, y) &isin; &mathbb{F} p &times; &mathbb{F} p : y 2 = x 3 + 1}. Which of the following statements is true?