Here is the official solution file: pen18.pdf

**A23** Prove that if

is expressed as a fraction, where is a prime, then divides the numerator.

**A24** Let be a prime number and . Prove that

is divisible by .

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**A13** Show that for all prime numbers ,

is an integer.

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C2 The positive integers and are such that the numbers and are both squares of positive integers. What is the least possible value that can be taken on by the smaller of these two squares?

Here is the official solution file: pen16.pdf

You can discuss the problem in MathLinks here.

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**C2** The positive integers and are such that the numbers and are both squares of positive integers. What is the least possible value that can be taken on by the smaller of these two squares?

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