On the Fundamental Theorem of Arithmetic and Euclid's Theorem
the infinitude of primes that rely on the Fundamental Theorem of Arithmetic. We discover this by carefully observing the set of primes involved in the statement.
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C.F. Gauss, Disquisitiones Arithmaticae, Leipzig (1801) [English translation by A.C.
Clarke, Yale Univ. Press (1966)]
S. Mac Lane and G. Birkhoff, Algebra, American Mathematical Society (1999)
L.J. Rips, “Circular reasoning”, Cognitive Science 26 (2002), 767–795
D. Varberg, E. Purcell, and S. Rigdon, Calculus, 9th ed., Pearson International Edition