\(a)2021\cdot2023\\ =\left(2022-1\right)\left(2022+1\right)\\ =2022^2-1< 2022^2\\ b)7^{16}-1\\ =\left(7^8+1\right)\left(7^8-1\right)\\ =\left(7^8+1\right)\left(7^4+1\right)\left(7^4-1\right)\\ =\left(7^8+1\right)\left(7^4+1\right)\left(7^2+1\right)\left(7^2-1\right)\\ =48\left(7^8+1\right)\left(7^4+1\right)\left(7^2+1\right)>8\left(7^8+1\right)\left(7^4+1\right)\left(7^2+1\right)\)