妙妙貓

The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, ....2The square numbers are 1, 4, 9, 16, 25, 36, 49, 64, ....With one exception, if a square number differs from a prime by 1, the prime is bigger.For example, 16 is a square and 17 is a prime. The prime is bigger. The only exception is prime 3 and square 4. It is conjectured that for all consecutive numbers that are a prime and a square, except for 3 and 4, the prime is bigger. Prove the conjecture is true.

I saw this question, and have no idea even how to approach it.

風之男

Proof by contradiction works here. Your textbook should have some tips on setting up proof by contradiction?

It's another "do more and learn more" situation.

Solution: https://docdro.id/Fg9zApC

[ 本帖最後由 風之男 於 2022-4-5 07:43 PM 編輯 ]

妙妙貓

Oh, that makes sense, thank you very much