Question: If p is prime and p | (a^2 + b^2) and p | (c^2 + d^2), then p | (a^2 + c^2) modern algebra- prove

If p is prime and p | (a^2 + b^2) and p | (c^2 + d^2), then p | (a^2 + c^2)

modern algebra- prove or disprove

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