Question

Tính giá trị biểu thức Q = 5³² - 24(5² + 1)(5⁸ + 1)(5¹⁶ +1)

Answer 1

\(626Q=\left(5^4+1\right)Q=5^{36}+5^{32}-\left(5^2-1\right)\left(5^2+1\right)626\left(5^8+1\right)\left(5^{16}+1\right)=5^{36}+5^{32}-\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)=5^{36}+5^{32}-\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)=5^{36}+5^{32}-\left(5^{16}-1\right)\left(5^{16}+1\right)=5^{36}+5^{32}-5^{32}+1=5^{36}+1=\left(5^{12}+1\right)\left(5^{24}-5^{12}+1\right)=\left(5^4+1\right)\left(5^8-5^4+1\right)\left(5^{24}-5^{12}+1\right)\Rightarrow Q=\left(5^8-5^4+1\right)\left(5^{24}-5^{12}+1\right)\)