Dr Reasoner (see challenges 160 and 173) is very excited about her new ideas concerning prime numbers.

Her first claim is that if p is a prime number, it is always possible to find a whole number n such that np + 1 is a square number. Is she right? If so, can you prove it? If not, can you adapt her claim to make it true?

Her second claim is that for any odd number n, there is always a prime p so that np + 1 is a square number. Can you prove (or disprove) her claim?