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I am instructed to define a recursive function in Python that finds the remainder of n divided by b with the condition to not use the "/" ,"%" or "//" operator. I have defined the following function, which works fine for positive numbers. Is there a better way to do this using recursion and simple conditions.

def division(n, b, q = 1):
 """
 parameters : a et b (integers)
 returns: the remainder of a and b
 pre-requisites : q = 1
 """
 if n <= 0 or n < b:
 if n == 0:
 print("Your division has no remainder.")
 elif n in range(0,5):
 print("Your remainder is", n)
 return 0
 else:
 return division(n - b, b, q) + q

print(division(274,5))

I believe your teacher was probably only trying to go for remainders without quotients.

def division(n, b):
 if n < b:
 return n
 return division(n - b, b)
print(division(274, 5))

However, since you brought it up, you can do it with the quotient, without having to start with a 1 for the default.

def division(n, b, q = 0):
 if n < b:
 return n, q
 return division(n - b, b, q + 1)
print(division(274, 5))

Main takeaways, you do not need to check n for range (0,5).

What about

def remainder(n, q):
 if(n < q):
 return n
 return remainder(n - q, q)

print(remainder(274, 5)) # will return: 4
print(remainder(275, 5)) # will return: 0
print(remainder(123, 3)) # will return: 0

much shorter ...