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Q. x²+y²if x and y are integers den hw many ordered pairs of x,y exist

[Wonder Boy]

First we consider positive integers pair

following pair satisfy the condition

1,1 = 2 ; 1,2 = 5 ; 1,3 = 10; 1,4 = 17 ; 1,5 = 26

2,1 = 5; 2,2 = 8 ; 2,3= 13 , 2,4 = 20 , 2,5 = 29

3,1 = 10; 3,2 = 13 ; 3,3 = 18 ; 3,4 = 25 ; 3,5 = 34

4,1 = 17; 4,2 = 20; 4,3 = 25; 4,4 = 32

5,1 = 26; 5,2 = 29; 5,3 = 34

 

SO total 22 pairs.

Now considering theor -ve values we get 22 x4 = 88 pairs

also for 0

pairs will be 0,1; 0,2;0,3;0,4;0,5 and 1,0; 2,0; 3,0; 4,0; 5,0 and their – ve values

total 20 pairs

 

and (0,0)

so total = 88 + 20 +1 = 109 Ans

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