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Fermat's little theorem

Fermat's little theorem. Fermat's little theorem states that if P is a prime number, then for any integer n ≥1. Theorem: ( FLT) : Let P is a prime number then, n P ≡ n(mod p). Fermat's little theorem. Corollary : Let P is a prime number then,

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Fermat's little theorem

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  1. Fermat's little theorem Fermat's little theorem states that if Pis a prime number, then for any integer n ≥1. Theorem: (FLT) : Let P is a prime number then, nP≡ n(mod p)

  2. Fermat's little theorem Corollary : Let P is a prime number then, nP-1≡ 1(mod p) For any integer n ≥1 with (n,p) = 1 H.C.F

  3. Fermat's little theorem Example: (FLT) : Let P is a prime number then, nP ≡ n(mod p) n = 5, p = 3 53 ≡ 5(mod 3) 125 ≡ 5(mod 3) 125-5 is divisible by 3 3/125-5 Corollary : Let P is a prime number then, nP-1 ≡ 1(mod p) For any integer n ≥1 with (n,p) = 1 53-1 ≡ 5(mod 3) 52 ≡ 5(mod 3) 25 ≡ 5(mod 3)

  4. Fermat's little theorem Example: (FLT) : Let P is a prime number then, nP ≡ n(mod p) n = 7, p = 2 72 ≡ 7(mod 2) 49 ≡ 7(mod 2) 49-7 is divisible by 2 2/49-7 Corollary : Let P is a prime number then, nP-1 ≡ 1(mod p) For any integer n ≥1 with (n,p) = 1 72-1 ≡ 7(mod 2) 71 ≡ 7(mod 2) 7 ≡ 7(mod 2)

  5. Fermat's little theorem • Activity: • n = 9, p = 3 • n = 15, p = 3 • n = 20, p = 2

  6. Fermat's little theorem Activity 1: (FLT) : Let P is a prime number then, nP ≡ n(mod p) n = 9, p = 3 93 ≡ 9(mod 3) 729 ≡ 9(mod 3) 729-9 is divisible by 3 3/729-9 Corollary : Let P is a prime number then, nP-1 ≡ 1(mod p) For any integer n ≥1 with (n,p) = 1 93-1 ≡ 1(mod 3) 92 ≡ 1(mod 3) 81 ≡ 1(mod 3)

  7. Fermat's little theorem Activity 2: (FLT) : Let P is a prime number then, nP ≡ n(mod p) n = 15, p = 3 153 ≡ 15(mod 3) 3375 ≡ 15(mod 3) 3375-15 is divisible by 3 3/3375-15 Corollary : Let P is a prime number then, nP-1 ≡ 1(mod p) For any integer n ≥1 with (n,p) = 1 153-1 ≡ 15(mod 3) 152 ≡ 15(mod 3) 225 ≡ 15(mod 3)

  8. Fermat's little theorem Activity 3: (FLT) : Let P is a prime number then, nP ≡ n(mod p) n = 20, p = 2 202 ≡ 20(mod 2) 400 ≡ 20(mod 2) 400-20 is divisible by 2 2/400-20 Corollary : Let P is a prime number then, nP-1 ≡ 1(mod p) For any integer n ≥1 with (n,p) = 1 202-1 ≡ 20(mod 2) 201 ≡ 20(mod 2) 20 ≡ 20(mod 2)

  9. Fermat's little theorem SUBMITTED TO: TEACHER :WENDEL GLENN JUMALON (MATHEMATICS TEACHER) SUBMITTED BY: 1.PHIPHATNAREE T.- NO.06 EP4/1 2.WARATCHAYA T.- NO.08 EP4/1 3.SUPARPICH S.- NO.32 EP4/1 4.SUPISSARA S.- NO.33 EP4/1

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