SOLUTION: Can you please help to answer the following question: . Find all positive integers a and b such that: a^2+b^2-7=ab

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At first,note that a^2+b^2-7=ab -->a^2+b^2 = ab +7.
So, if a,b are positive then a^2+b^2 > 7.

Convert a^2+b^2-7=ab to i.e.
. Hence,

Also, notice a & b are symmetric.
[note a,b are positive integers with and ]
Consider the table below (using Excel or direct computation)
a b a^2+b^2-ab
1 3 7
1 4 13
1 5 21
1 6 31
1 7 43
2 2 4
2 3 7 [No need to check a >= 3, why ?]
The only pairs (a,b) with satisfying a^2+b^2-ab = 7 are
(1,3) and (2,3). Hence,we also have (3,1) and (3,2)
So,there are 4 pairs of positive integer solutions:
(1,3),(2,3), (3,1) and (3,2)

Kenny