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Find the sum of all primes ppp for which the system
p+1=2x2p2+1=2y2\qquad \qquad p+1=2x^2 \\\qquad \qquad p^2+1=2y^2 p+1=2x2p2+1=2y2
has a solution in integers x,yx,yx,y.
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