return True Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. primitive root of 7. def findPrimefactors(s, n) : # Pr the number of 2s that divide n s = set(), # Check if n is prime or not Return -1 if n is a non-prime number. # This is checked so that we can skip while (y > 0): # If y is odd, multiply x with result # Check for every number from 2 to phi Start Here; Our Story; Hire a Tutor; Upgrade to Math Mastery. 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Primitive Root Calculator. if (power(r, phi // it, n) == 1): # If there was no power with value 1. Email: donsevcik@gmail.com Tel: 800-234-2933; Return -1 if n is a non-prime number. # value of Euler Totient function is n-1 findPrimefactors(s, phi). How to avoid overflow in modular multiplication? https://en.wikipedia.org/wiki/Primitive_root_modulo_n#Finding_primitive_roots Although there can be multiple primitive root for a prime number but we are only concerned for smallest one.If you want to find all roots then continue the process till p-1 instead of breaking up on finding first primitive root. for r in range(2, phi + 1): # Iterate through all prime factors of phi. A primitive root of a prime p is an integer g such that g (mod p) has multiplicative order p-1 (Ribenboim 1996, p. 22). x = (x * x) % p. # Utility function to store prime if (isPrime(n) == False): . If the multiplicative order of a number r modulo n is equal to Euler Totient Function Φ(n) (Note that Euler Totient Function for a prime n is n-1), then it is a primitive root [Source : Wiki]. If all these values are different, then return r, else continue for next value of r. If all values of r are tried, return -1. # factors of a number x = x % p # Update x if it is more for it in s: # Check if r^((phi)/primefactors) if (n % i == 0 or n % (i + 2) == 0) : return -1, # Find value of Euler Totient function return r, # Driver Code # of a given number n if (n <= 1): s.add(n), # Function to find smallest primitive # as there are n-1 relatively prime numbers. An efficient solution is based on below fact. Smallest number S such that N is a factor of S factorial or S! phi = n – 1, # Find prime factors of phi and store in a set This article is attributed to GeeksforGeeks.org. # middle five numbers in below loop Extended Keyboard; Upload; Examples; Random; Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions … for i in range(3, int(sqrt(n)), 2): # While i divides n, pr i and divide n # than or equal to p A primitive root mod n n n is an integer g g g such that every integer relatively prime to n n n is congruent to a power of g g g mod n n n. That is, the integer g g g is a primitive root (mod n n n) if for every number a a a relatively prime to n n n there is an integer z z z such that a ≡ (g z (m o d n)). s.add(2) i = 5 in O(logy) */""" Zeckendorf’s Theorem (Non-Neighbouring Fibonacci Representation), Find nth Fibonacci number using Golden ratio, n’th multiple of a number in Fibonacci Series, Space efficient iterative method to Fibonacci number, Factorial of each element in Fibonacci series, Fibonomial coefficient and Fibonomial triangle, An efficient way to check whether n-th Fibonacci number is multiple of 10, Find Index of given fibonacci number in constant time, Finding number of digits in n’th Fibonacci number, Count Possible Decodings of a given Digit Sequence, Program to print first n Fibonacci Numbers | Set 1, Modular Exponentiation (Power in Modular Arithmetic), Find Square Root under Modulo p | Set 1 (When p is in form of 4*i + 3), Find Square Root under Modulo p | Set 2 (Shanks Tonelli algorithm), Euler’s criterion (Check if square root under modulo p exists), Multiply large integers under large modulo, Find sum of modulo K of first N natural number. y = y >> 1 # y = y/2 Primitive Root Calculator. . Since we achieved all values from 1 to 6 in our residue results, then 3 is a primitive root of 7 Watch the Primitive Root Video. By using our site, you consent to our Cookies Policy. from math import sqrt. a \equiv \big(g^z \pmod{n}\big). def findPrimitive( n) : if (n % 2 == 0 or n % 3 == 0): while(i * i <= n): Primitive Root Video. Primitive root of a prime number n is an integer r between[1, n-1] such that the values of r^x(mod n) where x is in range[0, n-2] are different. """ Iterative Function to calculate (x^n)%p How to check if a given number is Fibonacci number? ), Count trailing zeroes in factorial of a number, Find the first natural number whose factorial is divisible by x, Count numbers formed by given two digit with sum having given digits, Generate a list of n consecutive composite numbers (An interesting method), Expressing factorial n as sum of consecutive numbers, Find maximum power of a number that divides a factorial, Trailing number of 0s in product of two factorials, Print factorials of a range in right aligned format, Largest power of k in n! (factorial) where k may not be prime, One line function for factorial of a number, Find all factorial numbers less than or equal to n, Find the last digit when factorial of A divides factorial of B, An interesting solution to get all prime numbers smaller than n, Calculating Factorials using Stirling Approximation, Check if a number is a Krishnamurthy Number or not, Find a range of composite numbers of given length. # n must be odd at this po. A simple solution is to try all numbers from 2 to n-1. def power( x, y, p): # mod n is 1 or not n = n // 2. # Python3 program to find primitive root n = 761 Email: donsevcik@gmail.com Tel: 800-234-2933; if (n > 2) : Given a prime number n, the task is to find its primitive root under modulo n. Primitive root of a prime number n is an integer r between[1, n-1] such that the values of r^x(mod n) where x is in range[0, n-2] are different. Number is Fibonacci number if you find anything incorrect, or you want to share information... 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