SOLUTION: Last year Jason's age was a prime number. This year it is a square number. How old is he this year?

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Question 1171548: Last year Jason's age was a prime number. This year it is a square number. How old is he this year?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
4,9,16,25,36,49,...?
One Less for each:
3,8,15,35,48,...?

One possibility is 3 years old last year, and 4 years old this year.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Let    be Jason's age this year (= current age).


The last year his age was  = p, some prime number.


But   = (n+1)*(n-1).


Since p is a prime number, it implies that n-1 = 1.


Hence, n = 2, and Jason's current age is   =  = 4 years.      ANSWER

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The first tutor missed the point of the problem; there is only one solution.

His age this year is a square number; let it be x^2.

That means last year his age was x^2-1.

But x^2-1 = (x-1)(x+1), which is the product of two integers. The only way the product of two integers can be prime is if one of them is 1.

So x-1 is 1, making x=2 and x+1=3. So his age last year was 1*3=3, making his age this year 4.
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