Which Is the Largest ?
Number Theory
Level
3
There are three successive odd integers such that their product is a prime number. Find the largest of the three numbers.
11
1
5
7
3
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By definition, a prime number's only factors are 1 and itself, so it looks like there might be a problem until you realise the three consecutive integers can include both − 1 and 1 . To get a positive result, an even number of these integers must be negative; the only triple that works is − 3 ⋅ − 1 ⋅ 1 = 3 .