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  • 03-02-2018
  • Mathematics
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Write the expression as a product of polynomials:

a(p–q)+q–p

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kaliyahbenning2
kaliyahbenning2 kaliyahbenning2
  • 05-02-2018
Solution: Since p 6= q are prime numbers, we have gcd(p, q) = 1. By Fermat’s Little Theorem, p q−1 ≡ 1 (mod q) . Clearly q p−1 ≡ 0 (mod q) . Thus p q−1 + q p−1 ≡ 1 (mod q) . Exchanging the roles of p and q in the above argument, we prove that p q−1 + q p−1 ≡ 1 (mod p)
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