Why does the Diophantine equation $A^5 + B^5 = C^5 + D^5$ seem attractive?

Addendum primum:

See also here.

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# $A^5 + B^5 = C^5 + D^5$

Why does the Diophantine equation $A^5 + B^5 = C^5 + D^5$ seem attractive?

Addendum primum:

See also here.

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