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Cube equal to a sum of three large cubes

Question

Find the integer xx satisfying x3=4413+5883+7353x^3=441^3+588^3+735^3.

Short answer

882882. The three numbers are 147⋅3147\cdot3, 147⋅4147\cdot4, 147⋅5147\cdot5, and 33+43+53=216=633^3+4^3+5^3=216=6^3. So x3=1473⋅63x^3=147^3\cdot6^3 and x=882x=882.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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