Only ? different right triangles have leg-lengths √a and √b and hypotenuse-length √2003, where a and b are integers are a>b?0.

A. 1001
B. 1002
C. 2002
D. 2003

a + b = 2003

a = 2003 -b

b could be 1 and a could be 2002
2 and 2001
3 and 2000
4 and 1999
I think I may get tired of this so
.
.
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1000 and 1003
1001 and 1002
oops then
1002 and 1001 b is bigger than a, no good
so 1001