Observe that: 6= 1 X2 X3; 24 = 2 X 3 X 4; 60 = 3 X 4 X 5 - Note also that: 6 = 23 - 2 ; 24 = 33 - 3 ; 60 = 43 - 4 (a) Write down the first number larger than 60 that is the product of three consecutive integers. (b) Write down the smallest 4-digit number that is the product of three consecutive integers. (c) Prove algebraically that any number that can be written in the form n - n can be expressed as the product of three consecutive integers.
