25 points!!!!!!!!!!!!!!!!!!!!!
2 answers:
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Consider expression
. If this expression becomes an integer, then b=4,9,16,25, because then 
2,3,4,5, respectively. In other cases 
is not integer and thus the expression also is not integer.
1. b=4, then
. Here a=2,7 (in other cases 
is not integer). When a=2, 
and when a=7, 
.
2. b=9, then a=6 and
.
3. b=16, then a=5 and
.
4. b=25, then a=4 and
.
Answer: (2,4), (7,4), (6,9), (5,16), (4,25).
Consider expression
1. b=4, then
2. b=9, then a=6 and
3. b=16, then a=5 and
4. b=25, then a=4 and
Answer: (2,4), (7,4), (6,9), (5,16), (4,25).