If you know that 144 is 12 squared, it would make sense to try 11 and 13. And viola!
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The two consecutive, odd integers whose product equals 143 are 11 and 13.
There is no solution. 3*5*7 = 105 is too small, and the next three 5*7*9 = 315 is too large.
Their product is 143.
Assuming three consecutive years of no more than 52 consecutive beginnings of a week, 143 weeks is equal to 143/52 = 2.75 years.
Other than itself and 1, the only positive integer factors of 143 are 13 x 11.