CODEWITHSUNDEEP
javaalgorithmdata-structuresfibonacci
dev-journey
dev-journey

Reputation: 39

Why is the pisano period of 11 equal to 120 and not 9

I am trying to find the pisano period of m=11 such that , fn mod m is repeats after that period, for 11, i noticed that most online forums mentioned that the pisano period for 11 is 120. code for finding pisano period here

However when trying to find the pisano period of 11, I am running into the following pattern for fn mod m :

n=0 , m=11,  fn =   0 , fnmodm   0
n=1 , m=11,  fn =   1 , fnmodm   1
n = 2 , m=11  fn = 1   fnmodm : 1
n = 3 , m=11  fn = 2   fnmodm : 2
n = 4 , m=11  fn = 3   fnmodm : 3
n = 5 , m=11  fn = 5   fnmodm : 5
n = 6 , m=11  fn = 8   fnmodm : 8
n = 7 , m=11  fn = 13   fnmodm : 2
n = 8 , m=11  fn = 21   fnmodm : 10
n = 9 , m=11  fn = 34   fnmodm : 1
n = 10 , m=11  fn = 55   fnmodm : 0
n = 11 , m=11  fn = 89   fnmodm : 1
n = 12 , m=11  fn = 144   fnmodm : 1
n = 13 , m=11  fn = 233   fnmodm : 2
n = 14 , m=11  fn = 377   fnmodm : 3
n = 15 , m=11  fn = 610   fnmodm : 5
n = 16 , m=11  fn = 987   fnmodm : 8
n = 17 , m=11  fn = 1597   fnmodm : 2
n = 18 , m=11  fn = 2584   fnmodm : 10
n = 19 , m=11  fn = 4181   fnmodm : 1
n = 20 , m=11  fn = 6765   fnmodm : 0
n = 21 , m=11  fn = 10946   fnmodm : 1
n = 22 , m=11  fn = 17711   fnmodm : 1
n = 23 , m=11  fn = 28657   fnmodm : 2
n = 24 , m=11  fn = 46368   fnmodm : 3
n = 25 , m=11  fn = 75025   fnmodm : 5
n = 26 , m=11  fn = 121393   fnmodm : 8
n = 27 , m=11  fn = 196418   fnmodm : 2
n = 28 , m=11  fn = 317811   fnmodm : 10
n = 29 , m=11  fn = 514229   fnmodm : 1
n = 30 , m=11  fn = 832040   fnmodm : 0
n = 31 , m=11  fn = 1346269   fnmodm : 1
n = 32 , m=11  fn = 2178309   fnmodm : 1
n = 33 , m=11  fn = 3524578   fnmodm : 2
n = 34 , m=11  fn = 5702887   fnmodm : 3
n = 35 , m=11  fn = 9227465   fnmodm : 5
n = 36 , m=11  fn = 14930352   fnmodm : 8
n = 37 , m=11  fn = 24157817   fnmodm : 2
n = 38 , m=11  fn = 39088169   fnmodm : 10
n = 39 , m=11  fn = 63245986   fnmodm : 1
n = 40 , m=11  fn = 102334155   fnmodm : 0

As you would notice that fnmodm repeats after every 10 values. Hence why is

Can some one please take a look and let me know what I am missing here?

Upvotes: 3

Views: 108

Answers (1)

Mirco Paul
Mirco Paul

Reputation: 131

The pattern you get seems correct. The Pisano period of 11 is 10.

Upvotes: 2

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