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Recursionmedium
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The Fibonacci sequence modulo 3 is defined by Fn≡Fn−1+Fn−2(mod3)F_n \equiv F_{n-1} + F_{n-2} \pmod{3}Fn​≡Fn−1​+Fn−2​(mod3) with F0≡0,F1≡1(mod3)F_0 \equiv 0, F_1 \equiv 1 \pmod{3}F0​≡0,F1​≡1(mod3). Compute the sequence and determine the period (the smallest positive ppp such that (Fp,Fp+1)≡(F0,F1)(mod3)(F_p, F_{p+1}) \equiv (F_0, F_1) \pmod{3}(Fp​,Fp+1​)≡(F0​,F1​)(mod3)).