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I tried solving the problem by factoring knowing that in order for the answer to be prime one of the factors had to be either one or negative (with the other being a negative value) by definition of a prime number. So i solved for n with each factor solved for 1 and -1 and plugged all those possible solutions back into the original equation. Working with Saskia was super helpful because she had made an awesome graph on Geogebra and was graph different prime y values trying to find where the corresponding x-value was an integer and so we were able to check our answers with each other.

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looking at this equation graphically to try and help

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multiple groups brought up ideas about how to start trying to solve for n such as guess and check or using derivatives

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finding formulas, number of solutions, graphing

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Lots of people are talking about how many solutions there are and if there's a pattern to them.

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multiple groups wondered how we could look at this though different lenses (graphing, algebra) and how those different lenses would help us understand the problem.

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lots of people had the idea of trying to find a formula to solve this

I found interesting that no one explicitly bought up factoring because I know Mari and I discussed that but decided to post different questions

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Similarities: graphing to solve the problem, infinite possibilities, and and fining an equation to help solve. Can graphing help us find the equation?
Differences: I notices Saskia and Silas asked if it was related to derivatives which I hadn't thought about

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1)how many possibilities are there?
2) is it easier to find qualities that n has to have, or just guess and check numbers?
3) what numbers can n not be?

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1. can we solve the problem by graphing?
2. Are there an infinite number of solutions?

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1) Is there a formula/pattern to find prime number answers?
2) Is there a way to manipulate the equation to a form that will tell us something about when you would get prime number answers?
3) Is this related to derivatives?

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1.) Is there an easier way to solve this than just guess and check with every prime number? How would we set the equation up to do so and to get the set of answers as an expression?
2.) Would graphing help?
3.) How would the amount of solutions change if the constants were changed?

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i am excited to have class with you all today