Unformatted text preview: p 1 and p 2 be prime. Is p 1 × p 2 + 1 always prime? Give a proof or counter example. (b) For some prime p , is p1 (mod p ) ever a perfect square? 4. Show that there is always a onetoone and onto mapping between any two countably inﬁnite sets. Make sure to use a well deﬁned function as your mapping, ie the identity mapping, for some set S , f : S → S where f ( s ) = s . 5. We want to show that the set of reals and the set of pairs of reals have the same cardinality. Note we cannot list the reals so we can’t talk about the i th real mapping to the j th real pair. Instead, construct a onetoone and onto mapping, f : R → R 2 . 1...
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 '07
 SELMAN
 Number Theory, Square number

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