SOLUTION: For the equation {{{ (a-b)^2 + a^2 = 169 }}} a and b are integers, and a≥0. Find the number of different ordered pairs (a,b) that occur.

Question 1189240: For the equation a and b are integers, and a≥0. Find the number of different ordered pairs (a,b) that occur.
Found 2 solutions by Alan3354, pademin:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
For the equation a and b are integers, and a≥0. Find the number of different ordered pairs (a,b) that occur.
-------------

5^2 + 12^2 = 169
---
a = 12, b = 7
a = 5, b = -7
a = 0, b = 13
a = 0, b = -13
----------
Might be others, but I doubt it.

Answer by pademin(1) (Show Source): You can put this solution on YOUR website!
There are 7 integer solutions in total.
================
a = 0, b = -13
a = 0, b = 13
a = 5, b = -7
a = 5, b = 17
a = 12, b = 7
a = 12, b = 17
a = 13, b = 13
RELATED QUESTIONS
For the equation (a-b)^2+a^2=25, a and b are integers and a ≥ 0. List the ordered... (answered by Boreal,Edwin McCravy)
For the equation (a-b)^2 + a^2 = 625, a and b are integers and a≥0. List the ordered... (answered by greenestamps)
Find the number of ordered pairs (a,b) of integers such that \frac{a + 2}{a + 5} =... (answered by ikleyn)
For the equation (a-b)^2 + a^2 = 25, a and b are integers and a is greater than or equal... (answered by ikleyn)
For the equation {{{(a-b)^2 + a^2 = 289}}}, a and b are integers and a is more than or... (answered by greenestamps)
Determine the number of ordered pairs of positive integers (a,b) such that a and b are... (answered by greenestamps)
find the ordered pairs that are both solutions of the given equation: 3x=5y+2 A)(5,3)... (answered by MathLover1)
How many ordered pairs (a,b) of positive integers satisfy a^2 + b^2 = 50 (answered by vleith)
Two cards are drawn from a standard deck of 52 cards. What is the probability that a king (answered by stanbon,Edwin McCravy)