In theory you can, by simulating individual data structures or even the entire memory (static data, heap and stack) with arrays. But the question is whether this is very practical; it may involve having to rewrite every pointer-based standard library function you need.
Anyway, there’s a nice explanation on Wikipedia:
It is possible to simulate pointer behavior using an index to an (normally one-dimensional) array.
Primarily for languages which do not support pointers explicitly but do support arrays, the array can be thought of and processed as if it were the entire memory range (within the scope of the particular array) and any index to it can be thought of as equivalent to a general purpose register in assembly language (that points to the individual bytes but whose actual value is relative to the start of the array, not its absolute address in memory). Assuming the array is, say, a contiguous 16 megabyte character data structure, individual bytes (or a string of contiguous bytes within the array) can be directly addressed and manipulated using the name of the array with a 31 bit unsigned integer as the simulated pointer (this is quite similar to the C arrays example shown above). Pointer arithmetic can be simulated by adding or subtracting from the index, with minimal additional overhead compared to genuine pointer arithmetic.
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solved C program with pointer