# how old am I

#### bekah24h

##### New member
How old am I? My age is a perfect square number of years greater than a perfect square number; it is also a perfect square number of years less than a perfect square. Next year, my age will be a prime number less than 50

#### Subhotosh Khan

##### Super Moderator
Staff member
bekah24h said:
How old am I? My age is a perfect square number of years greater than a perfect square number; it is also a perfect square number of years less than a perfect square. Next year, my age will be a prime number less than 50
Next year, my age will be a prime number less than 50

Does the sentence above mean:

Next year, my age will be a prime number - less than 50

Next year, my age will be - a prime number less than 50

In either case:

Let my age = A

Now continue.....

Please show us your work/thoughts, indicating exactly where you are stuck - so that we may know where to begin to help you.

#### soroban

##### Elite Member
Hello, bekah24h!

How old am I?
My age is a perfect square number of years greater than a perfect square number.
It is also a perfect square number of years less than a perfect square.
Next year, my age will be a prime number less than 50.

There is no formula for this type of problem.
. . We must resort to intelligent guesswork.

Let $$\displaystyle A$$ = my age.

$$\displaystyle \text{Then: }\;\begin{array}{ccccc}A\text{ is the sum of two squares:} & A &=& a^2+b^2 \\ A\text{ is the difference of two squares:} & A &=& c^2-d^2 \end{array}$$

Consider the square numbers:

. . $$\displaystyle \begin{array}{ccccccccccccccc}1 & \boxed{4} & 9 & 16 & 25 & \boxed{36} & 49 & 64 & \boxed{81} & 100 & \boxed{121} & 144 & 169 & \hdots$$
. . . .. $$\displaystyle \underbrace{\qquad\qquad\qquad\qquad\quad}_{\text{sum of 40}} \qquad\qquad\quad \underbrace{\qquad\qquad\qquad\quad}_{\text{difference of 40}}$$

Therefore, my age is 40.