Sure, here is a simple program in Python that implements the FizzBuzz problem:
```
for i in range(1, 101):
    if i % 3 == 0 and i % 5 == 0:
        print("FizzBuzz")
    elif i % 3 == 0:
        print("Fizz")
    elif i % 5 == 0:
        print("Buzz")
    else:
        print(i)
```
This program uses the modulo operator % to check if a number is divisible by 3 and/or 5, and then prints the appropriate output based on that. It also demonstrates how to use if-elif-else statements, the range function, and the print function in Python.
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