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

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In summary, the equation $3p^4-5q^4-4r^2=26$ can be solved for the variables $p$, $q$, and $r$, and there are an infinite number of solutions for $(p,q,r)$. It cannot be solved for just one variable and typically, techniques such as substitution, elimination, or using a system of equations are used to solve for $(p,q,r)$. It is important to note that there may be multiple solutions for $(p,q,r)$.
  • #1
Albert1
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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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  • #2
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 : $q^4-r^2\equiv -1 \,\,(mod \,\, 3)$
 

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

1. What is the equation for solving for $(p,q,r)$ when $3p^4-5q^4-4r^2=26$?

The equation for solving for $(p,q,r)$ is $3p^4-5q^4-4r^2=26$.

2. What are the variables in the equation $3p^4-5q^4-4r^2=26$?

The variables are $p$, $q$, and $r$.

3. How many solutions are there for $(p,q,r)$ in the equation $3p^4-5q^4-4r^2=26$?

There are an infinite number of solutions for $(p,q,r)$ in this equation.

4. Can the equation $3p^4-5q^4-4r^2=26$ be solved for just one variable?

No, this equation cannot be solved for just one variable. All three variables $p$, $q$, and $r$ are necessary to find a solution.

5. How is this equation typically solved for $(p,q,r)$?

This equation can be solved through techniques such as substitution, elimination, or using a system of equations. It is important to note that there may be multiple solutions for $(p,q,r)$.

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