Question

Is there a solution in natural numbers to the equation `x^2 + 12 = y^3` such that

a. x is even (easier)

b. x is odd

Difficulty level (1 very easy - 10 very hard): 7

Number Theory -> Prime Numbers Number Theory -> Modular Arithmetic / Remainder Arithmetic Number Theory -> Division -> Parity (Even/Odd) Proof and Example -> Proof by Contradiction Arithmetic -> Division with Remainder Algebra -> Equations -> Diophantine Equations

Sources:

Mink Exercises and Additional Competition Materials, 2018-2019, Exercise 3 Question 6

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