Consider an integer > 1 with the following standard prime factorization:
= 2^ ⋅ 3 ^ ⋅ 5^ c where , , c ∈ ℤ ^+
a) Write the definition of the statement, "14 | " i.e. "14 divides "
b) Prove the following statement
∀ ,, c ∈ ℤ ^+,14 ∤ (2 ^ ⋅ 3 ^ ⋅ 5^c )
using Method of Contradiction using the uniqueness of "standard prime factorization" by first replacing 14 by its standard prime factorization (SPF) in the equation obtained in part a)
Proof by the Method of Contradiction: