Happy Mathday!

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Because I am too busy blowing out candles today, my tall, dark, handsome, and incredibly geeky fabulous boyfriend took it upon himself to “guest blog” for me. Here is the product, wherein he demonstrates how I am in the square prime of my life. Enjoy!

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While lying in bed with my sexy girlfriend on the morning of her birthday, I noted that her age is now the product of a prime number and a square. For a review for those who haven’t thought about math since Mr. Johnson kicked you out of Analytical Geometry for being drunk (oh wait, that was me), a prime is a number only divisible by one and itself (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 …), and a square is the product of a number times itself (4, 9, 16, 25, 36 …)
Of course, knowing her own age, she was able to determine the numbers in question. Let’s call them p1 and s1. Without having figured out the answer yet, I postulated, “When is the next time that will happen?” Giving up all too quickly to befit her geek creds, she said she didn’t know. When I told her it would happen next year, she thought about it for a few seconds and said, “You mean p2 and s2?”
Now p2 is a prime, and s2 is a square, but the product of them is not her age next year. The sum of them is! “Wow!” I thought, that’s really interesting, next year is her age not only the product of a square and a prime, but also the sum! (So there is also p3 and s3, which were the ones I thought of that work if you multiply them.)
So after a reasonable amount of birthday canoodling, I get up to take a shower. And of course the brain is still cranking away with squares and primes, when I realize that next year, there will be another Square Prime set where the sum will be her age, AND this year there is a set where the sum is her age! When will the madness end?
So for those who always thought the hardest part of the story problems was putting them into equations, I’ll do that part for you:
p1 * s1 = Age this year
p2 + s2 = Age next year
p3 * s3 = Age next year
p4 + s4 = Age next year
p5 + s5 = Age this year
One of the really neat things about this is that it works for you too! That is, when you are Jodi’s age, all of the figures will still work. But it is unlikely that any of us will work our figures the way Jodi does, nor have a figure that works so well.
Please have your answers submitted by the beginning of class next Friday.