Python | sympy.reduced_totient() method

With the help of sympy.reduced_totient() method, we can find the Carmichael reduced totient function or lambda(n) in SymPy. reduced_totient(n) or is the smallest m > 0 such that for all k relatively prime to n.

Syntax: reduced_totient(n) Parameter: n – It denotes an integer. Returns: Returns the smallest integer m > 0 such that k^m % n is equal to 1 for all k relatively prime to n.

Example #1:

# import reduced_totient() method from sympy
from sympy.ntheory import reduced_totient

n = 8

# Use reduced_totient() method
reduced_totient_n = reduced_totient(n)

print("lambda({}) =  {} ".format(n, reduced_totient_n))
# 1 ^ 2 = 1 (mod 8), 3 ^ 2 = 9 = 1 (mod 8),
# 5 ^ 2 = 25 = 1 (mod 8) and 7 ^ 2 = 49 = 1 (mod 8)

Output:

lambda(8) =  2 

Example #2:

# import reduced_totient() method from sympy
from sympy.ntheory import reduced_totient

n = 30

# Use reduced_totient() method
reduced_totient_n = reduced_totient(n)

print("lambda({}) =  {} ".format(n, reduced_totient_n))

Output:

lambda(30) =  4