The number of solutions of the equation $x ^2+ y ^2= a ^2+ b ^2+ c ^2$. where $x , y , a , b , c$ are all prime numbers, is

  • [KVPY 2021]
  • A

    $0$

  • B

    $1$

  • C

    more than $1$ but finite

  • D

    infinite

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  • [AIEEE 2002]