I’m thinking of a number, and one more than its square is a prime number. What can you tell me for certain about the number?

I’m thinking of a number, and one less than its square is a prime number. What can you tell me for certain about that number?

Imagine a group of young students, but old enough to play with these questions. How would you guide them?

And, oh yeah, what answers would you expect?

How far could you go with kids who don’t work with variables for the second question?

1. July 2, 2008 pm31 7:51 pm 7:51 pm

list the first dozen examples or so, natch.
how then to get into modular arithmetic?
–beats me. i almost never get to *play* with children!
as for the second … we’re already using a variable
as soon as we say “i’m thinking of a number” …
but i do take your point (i think): is there anything
interesting going on here if one *doesn’t* have
x^2 – 1 = (x+1)(x-1) ready-to-hand?

2. July 2, 2008 pm31 9:13 pm 9:13 pm

I am wondering if we could prompt them to factor a few off the second list. 0, 3, 8, boring, but 15, 24, 35, 48, 63…

Maybe 15, 35 get the brains moving, 99? interesting. If they get up to 143….

And then a geometric demo?

3. July 6, 2008 am31 7:42 am 7:42 am

Its ovious the answer. Im 13 and the answer (4) was ovious to me.(but im in G/T)I go to school in Louisiana.

4. July 6, 2008 pm31 8:09 pm 8:09 pm

Jason,

which problem were you trying to answer?

4 might not be the answer to either one. Can you say what you were trying to find? You could be close.