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Number Theory Exercise 1 Prove that the equation 3x^2 + 2 = y^2 has no solution (x,...

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Advance Math

Number Theory

Exercise 1 Prove that the equation 3x^2 + 2 = y^2 has nosolution (x, y) ? Z × Z. (Hint: consider the associated congruencemodulo 3.)

Exercise 2 Prove that the equation 7x^3 + 2 = y^3 has nosolution (x, y) ? Z × Z. (Hint: consider the associated congruencemodulo 7.)

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