| Text | Theorem: Let p be a prime number, let a ∈ {{{c1::1}},...,p−1}, and let b ∈ {{{c1::0}},...,p−1}. The function f:{{{c1::0}},...,p−1} to {{{c1::0}},...,p−1} given by the formula f(x) = (ax+b)%p is a {{c2::1-1 correspondence}}, i.e., every linear function mod p that is not constant mod p is a {{c2::1-1 correspondence}} from {{{c1::0}},...,p−1} to {{{c1::0}},...,p−1}. |
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| Text | A statement containing a {{c1::free}} variable x is {{c2::a}} statement about x.Renaming a {{c1::free}} variable in a sentence {{c2::changes}} the sentence’s meaning, {{c3::unless the statement is identically true}}.A statement containing a {{c1::bound}} variable x is {{c2::not a}} statement about x.Renaming a {{c1::bound}} variable in a sentence {{c2::does not}} change the sentence’s meaning, {{c3::unless the new variable name becomes overloaded}}. |
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| Text | There is/are exactly {{c1::1}} pair(s) (x,y) such that x and y ≡ {{c2::true}} |
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