Write a C program that declares an array of length N containing integers between 1 and N, determine if it contains any duplicates.

Have first a look to 'Solution 2'. It is much easier and universal and in general better ;)

This is your task to solve to learn c.
Therefore I will not give you the solution, but a hint.

Instanciate two arrays of integers, both with the size N.
Let's name them:

Values    // The values you need to evalate
Counts   // Don't forget to initialize all elements with 0

Values will hold the numbers you need to evaluate.
Loop over Values and count the corresponding number in Counts. Something like:

countIx= Values[valueIx] - 1;  // Think about why here '-1'
Counts[countIx]= Counts[countIx] + 1;

After all that you can loop over Counts and e.g. show how many time a number occured in Values.

Hint: What is fundamental here is that the indices of the array Count have a unique relationship to the values in Values. Try to understand the relationship, it has to do with the '-1' mentioned above.

[Edit]
Important: Be aware, this solution works only because of the restriction that the numbers to evaluate need to be in the range 1...N.

I hope it gives you an idea.