Question 1209470
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This is something to find through trial-and-error. 
Or you can use technology.


Of the integers in the interval 150 < x < 200, only the values 170 and 185 have two distinct ways to break them down into a sum of two squares
170 = 1+169 = 49+121
185 = 16+169 = 64+121
I'll assume that 0 isn't being considered. 


Therefore 185-170 = <font color=red>15</font> is the final answer.
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