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Find the number of integer solutions to a^2 + b^2 = 625.

May 14, 2020

#1
+25565
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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: $$7^2+24^2 = 25^2\quad \text{ (See: Pythagorean triple )}$$

May 14, 2020
edited by heureka  May 14, 2020

#1
+25565
+2

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: $$7^2+24^2 = 25^2\quad \text{ (See: Pythagorean triple )}$$

heureka May 14, 2020
edited by heureka  May 14, 2020