+26367 Find the number of integer solutions to \(a^2 + b^2 = 625\).
\(\begin{array}{|rclcrcl|} \hline a^2 + b^2 &=& 625& \text{or}& \mathbf{a^2 + b^2} &=& \mathbf{25^2} \\ \hline \end{array} \)
\(\begin{array}{|rcll|} \hline \mathbf{3^2+4^2} &=& \mathbf{5^2} \\\\ (3*5)^2+(4*5)^2 &=& (5*5)^2 \\ \mathbf{15^2+20^2} &=& \mathbf{25^2} \\ \hline \end{array}\)
\(a=15~ \text{and}~ b= 20 \)
There are other solutions for example: \(7^2+24^2 = 25^2\quad \text{ (See: Pythagorean triple )}\)
+26367 Find the number of integer solutions to \(a^2 + b^2 = 625\).
\(\begin{array}{|rclcrcl|} \hline a^2 + b^2 &=& 625& \text{or}& \mathbf{a^2 + b^2} &=& \mathbf{25^2} \\ \hline \end{array} \)
\(\begin{array}{|rcll|} \hline \mathbf{3^2+4^2} &=& \mathbf{5^2} \\\\ (3*5)^2+(4*5)^2 &=& (5*5)^2 \\ \mathbf{15^2+20^2} &=& \mathbf{25^2} \\ \hline \end{array}\)
\(a=15~ \text{and}~ b= 20 \)
There are other solutions for example: \(7^2+24^2 = 25^2\quad \text{ (See: Pythagorean triple )}\)
