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One of my favorite math problems that is easy to solve with just algebra:
Prove that 8 is the only perfect cube to follow a prime number.
If you don't know what a perfect cube is, that is simple, it is any integer raised to the power of 3. Since \(8 = 2^3\) it is a perfect cube, and it follows the number 7, which is prime. 8 is the only number that fits those conditions... prove it.
NOTE: I will give the answer as a reply. If anyone else wants to provide an answer please make sure you use a content warning.
@freemo is it required to follow a prime as part of the definition?
@Absinthe What do you mean? We are looking for a perfect cube that follows a prime and proving 8 is the **only** one.
@freemo okay, that was my question. My intuition says that it is so, and you say it is so, that is proof enough for me :)
@freemo okay and 0 is not prime