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

 May 14, 2020

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 #1
avatar+24909 
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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: \(7^2+24^2 = 25^2\quad \text{ (See: Pythagorean triple )}\)

 

laugh

 May 14, 2020
edited by heureka  May 14, 2020
 #1
avatar+24909 
+2
Best Answer

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

 

laugh

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

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