MHB Solving for $(p,q,r)$ When $3p^4-5q^4-4r^2=26$

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$p,q,r$ are all primes ,and $3p^4-5q^4-4r^2=26$

find $(p,q,r)=?$
 
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Albert said:
$p,q,r$ are all primes ,and $3p^4-5q^4-4r^2=26---(1)$

find $(p,q,r)=?$
hint:
(1) mod 3 we have : $q^4-r^2\equiv -1 \,\,(mod \,\, 3)$
 

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