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So, λ 1 k λ 2 k ≡ 1 mod p and λ 1 l λ 2 l ≡ 1 mod p. In other words, by considering the sums presented in (3), a k z k − b k c k ≡ 1 mod p ⟹ a k z k = p t 1 + 1 + b k c k. and a l z l − b l c l ≡ 1 mod p ⟹ a l z l = p t 2 + 1 + b l c l, for some integers t 1 and t 2. Hence, by applying side by removing, we get a k z k − b k c k ≡ a l z l − b l c l mod p, (9).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com