SOLUTION: Hi, I am having trouble with this question:
Find all possible sets of 4 consecutive integers such that the sum of the cubes of the smallest three is the cube of the fourth.
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Problems-with-consecutive-odd-even-integers
-> SOLUTION: Hi, I am having trouble with this question:
Find all possible sets of 4 consecutive integers such that the sum of the cubes of the smallest three is the cube of the fourth.
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Question 490715: Hi, I am having trouble with this question:
Find all possible sets of 4 consecutive integers such that the sum of the cubes of the smallest three is the cube of the fourth.
I tried forming an equation: x^3 + (x+1)^3 + (x+2)^3 = (x + 3)^3
But then I got stumped.
Can you please help? Answer by richard1234(7193) (Show Source):
From here, we can tell that x = 3 works. If you divide both sides of the previous equation by x-3 (either by synthetic or long division) we can find the other two roots:
The discriminant is negative, so there are no more integer roots. Hence x=3 --> {3,4,5,6} is the only solution.
