Plato's number or numbers?

Algebra Level 4

Let a , b , c , d a,b,c,d be 4 positive integers such that

  • They follows an arithmetic progression (in that order),
  • a 3 + b 3 + c 3 = d 3 a^3 + b^3 + c^3 = d^3 , and
  • gcd ( a , b , c , d ) = 1 \gcd(a,b,c,d) = 1 .

One possible solution of ( a , b , c , d ) = ( 3 , 4 , 5 , 6 ) (a,b,c,d) = (3,4,5,6) . Is there any other solution?

Yes, infinitely many No Yes, only finitely many

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