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Pachacha [2.7K]
3 years ago
6

Prove that there are no positive perfect cubes less than 1000 that are the sum of the cubes of two positive integers?

Mathematics
1 answer:
valentina_108 [34]3 years ago
6 0

The perfect cubes less than 1000 are: 

<span>1^3 = 1 </span>
<span>2^3 = 8 </span>
<span>3^3 = 27 </span>
<span>4^3 = 64 </span>
<span>5^3 = 125 </span>
<span>6^3 = 216 </span>
<span>7^3 = 343 </span>
<span>8^3 = 512 </span>
<span>9^3 = 729 
</span>
so 
<span>2^3 = 8 could only be 1 + 1, but this is 2, not 8. </span>
<span>3^3 = 27 could be 1 + 1, 1 + 8 or 8 + 8, but all of these are too small </span>
4^3 = 64 could be 1 + 1, 1 + 8, 1 + 27, 8 + 8, 8 + 27, 27 + 27.
<span> general proof that a^3 + b^3 = c^3 holds for no positive integers 
</span>hope it helps
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