Question: determine whether the statement is true or false any product...
Determine whether the statement is true or false.
Any product of four consecutive integers is one less than a perfect square.
Justify your answer with a proof or a counterexample, as appropriate. Use only the definitions of the terms and laws of algebra to justify the statements in your proof.
Two integers are consecutive if, and only if, one is one more than the other.
𝑎, 𝑏 𝑐𝑜𝑛𝑠𝑒𝑐𝑢𝑡𝑖𝑣𝑒 ↔ (𝑎 + 1 = 𝑏) ∨ (𝑏 + 1 = 𝑎)
Note: An integer 𝑎 is a perfect square if and only if it equals the square of an integer.
𝑎 ∈ 𝑍 𝑖𝑠 𝑎 𝑝𝑒𝑟𝑓𝑒𝑐𝑡 𝑠𝑞𝑢𝑎𝑟𝑒 ↔ ∃𝑏 ∈ 𝑍 | 𝑎 = 𝑏 2