試說明對於任意整數n,多項式(4n+5)^2-9一定能被8整除.

試說明對於任意整數n,多項式(4n+5)^2-9一定能被8整除.

(4n + 5)²;- 9= 16n²;+ 40n + 25 - 9= 16n²;+ 40n + 16= 8(2n²;+ 5n + 2)因為n是整數所以2n²;+ 5n + 2也是整數所以8(2n²;+ 5n + 2)一定能被8整除.所以(4n + 5)²;- 9一定…