South African Mathematics Olympiad Second Round

Question

If the product of four consecutive integers is equal to the value of one of those integers, then what is the largest possible value for any of the integers?

Accepted Answer

3

With a little trial and error it should soon be clear that this scenario is only possible if one of the integers is zero. The options are

- 3

;

- 2

;

- 1

;

0

or

- 2

;

- 1

;

0

;

1

or

- 1

;

0

;

1

;

2

or

0

;

1

;

2

;

3

. The largest possible integer is thus

3

.