RMO 3
Number Theory
Level
1
If N is an integer, what is the largest integer that is divisible by
N(N+1)(N+2)(N+3)?
2
4
16
24
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1 solution
see since the product is of 4 consecutive numbers there will be a multiple of 3 as if we take any one to yield any remainder one of the 4 will be divisible by 3 , now there will be consecutive even numbers and of 2 consecutive even numbers one is multiple of 2 and other of 4. so the product of 4 consecutive numbers will be divisible by 24