Well, I guess it is ok to give you more info...
Using the limits of c here are the limits of b.
If c = 26 then 25.62 <= b <= 36.24 --- 26 <= b <= 26
If c = 27 then 25.10 <= b <= 35.50 --- 26 <= b <= 27
If c = 28 then 24.55 <= b <= 34.71 --- 25 <= b <= 28
If c = 29 then 23.96 <= b <= 33.88 --- 24 <= b <= 29
If c = 30 then 23.33 <= b <= 33.00 --- 24 <= b <= 30
If c = 31 then 22.67 <= b <= 32.06 --- 23 <= b <= 31
If c = 32 then 21.97 <= b <= 31.06 --- 22 <= b <= 31
If c = 33 then 21.21 <= b <= 30.00 --- 22 <= b <= 30
If c = 34 then 20.41 <= b <= 28.86 --- 21 <= b <= 28
If c = 35 then 19.54 <= b <= 27.64 --- 20 <= b <= 27
If c = 36 then 18.61 <= b <= 26.32 --- 19 <= b <= 26
If c = 37 then 17.61 <= b <= 24.90 --- 18 <= b <= 24
If c = 38 then 16.51 <= b <= 23.35 --- 17 <= b <= 23
If c = 39 then 15.30 <= b <= 21.63 --- 16 <= b <= 21
If c = 40 then 13.95 <= b <= 19.72 --- 14 <= b <= 19
If c = 41 then 12.41 <= b <= 17.55 --- 13 <= b <= 17
If c = 42 then 10.61 <= b <= 15.00 --- 11 <= b <= 15
If c = 43 then 8.37 <= b <= 11.83 --- 9 <= b <= 11
If c = 44 then 5.15 <= b <= 7.28 --- 6 <= b <= 7
From that here are the 113 values of b and c you would have to check for integer values of a. Using a spreedsheet tool like excel or google docs it is easy to find the 11 unique sets of [a,b,c].
[?, b, c] : 1989 - c^2 - b^2 = a^2
[?,26,26] : 1989 - 26^2 - 26^2 = a^2
[?,26,27] : 1989 - 27^2 - 26^2 = a^2
[?,27,27] : 1989 - 27^2 - 27^2 = a^2
[?,25,28] : 1989 - 28^2 - 25^2 = a^2
[?,26,28] : 1989 - 28^2 - 26^2 = a^2
[?,27,28] : 1989 - 28^2 - 27^2 = a^2
[?,28,28] : 1989 - 28^2 - 28^2 = a^2
[?,24,29] : 1989 - 29^2 - 24^2 = a^2
[?,25,29] : 1989 - 29^2 - 25^2 = a^2
[?,26,29] : 1989 - 29^2 - 26^2 = a^2
[?,27,29] : 1989 - 29^2 - 27^2 = a^2
[?,28,29] : 1989 - 29^2 - 28^2 = a^2
[?,29,29] : 1989 - 29^2 - 29^2 = a^2
[?,24,30] : 1989 - 30^2 - 24^2 = a^2
[?,25,30] : 1989 - 30^2 - 25^2 = a^2
[?,26,30] : 1989 - 30^2 - 26^2 = a^2
[?,27,30] : 1989 - 30^2 - 27^2 = a^2
[?,28,30] : 1989 - 30^2 - 28^2 = a^2
[?,29,30] : 1989 - 30^2 - 29^2 = a^2
[?,30,30] : 1989 - 30^2 - 30^2 = a^2
[?,23,31] : 1989 - 31^2 - 23^2 = a^2
[?,24,31] : 1989 - 31^2 - 24^2 = a^2
[?,25,31] : 1989 - 31^2 - 25^2 = a^2
[?,26,31] : 1989 - 31^2 - 26^2 = a^2
[?,27,31] : 1989 - 31^2 - 27^2 = a^2
[?,28,31] : 1989 - 31^2 - 28^2 = a^2
[?,29,31] : 1989 - 31^2 - 29^2 = a^2
[?,30,31] : 1989 - 31^2 - 30^2 = a^2
[?,31,31] : 1989 - 31^2 - 31^2 = a^2
[?,22,32] : 1989 - 32^2 - 22^2 = a^2
[?,23,32] : 1989 - 32^2 - 23^2 = a^2
[?,24,32] : 1989 - 32^2 - 24^2 = a^2
[?,25,32] : 1989 - 32^2 - 25^2 = a^2
[?,26,32] : 1989 - 32^2 - 26^2 = a^2
[?,27,32] : 1989 - 32^2 - 27^2 = a^2
[?,28,32] : 1989 - 32^2 - 28^2 = a^2
[?,29,32] : 1989 - 32^2 - 29^2 = a^2
[?,30,32] : 1989 - 32^2 - 30^2 = a^2
[?,31,32] : 1989 - 32^2 - 31^2 = a^2
[?,22,33] : 1989 - 33^2 - 22^2 = a^2
[?,23,33] : 1989 - 33^2 - 23^2 = a^2
[?,24,33] : 1989 - 33^2 - 24^2 = a^2
[?,25,33] : 1989 - 33^2 - 25^2 = a^2
[?,26,33] : 1989 - 33^2 - 26^2 = a^2
[?,27,33] : 1989 - 33^2 - 27^2 = a^2
[?,28,33] : 1989 - 33^2 - 28^2 = a^2
[?,29,33] : 1989 - 33^2 - 29^2 = a^2
[?,30,33] : 1989 - 33^2 - 30^2 = a^2
[?,21,34] : 1989 - 34^2 - 21^2 = a^2
[?,22,34] : 1989 - 34^2 - 22^2 = a^2
[?,23,34] : 1989 - 34^2 - 23^2 = a^2
[?,24,34] : 1989 - 34^2 - 24^2 = a^2
[?,25,34] : 1989 - 34^2 - 25^2 = a^2
[?,26,34] : 1989 - 34^2 - 26^2 = a^2
[?,27,34] : 1989 - 34^2 - 27^2 = a^2
[?,28,34] : 1989 - 34^2 - 28^2 = a^2
[?,20,35] : 1989 - 35^2 - 20^2 = a^2
[?,21,35] : 1989 - 35^2 - 21^2 = a^2
[?,22,35] : 1989 - 35^2 - 22^2 = a^2
[?,23,35] : 1989 - 35^2 - 23^2 = a^2
[?,24,35] : 1989 - 35^2 - 24^2 = a^2
[?,25,35] : 1989 - 35^2 - 25^2 = a^2
[?,26,35] : 1989 - 35^2 - 26^2 = a^2
[?,27,35] : 1989 - 35^2 - 27^2 = a^2
[?,19,36] : 1989 - 36^2 - 19^2 = a^2
[?,20,36] : 1989 - 36^2 - 20^2 = a^2
[?,21,36] : 1989 - 36^2 - 21^2 = a^2
[?,22,36] : 1989 - 36^2 - 22^2 = a^2
[?,23,36] : 1989 - 36^2 - 23^2 = a^2
[?,24,36] : 1989 - 36^2 - 24^2 = a^2
[?,25,36] : 1989 - 36^2 - 25^2 = a^2
[?,26,36] : 1989 - 36^2 - 26^2 = a^2
[?,18,37] : 1989 - 37^2 - 18^2 = a^2
[?,19,37] : 1989 - 37^2 - 19^2 = a^2
[?,20,37] : 1989 - 37^2 - 20^2 = a^2
[?,21,37] : 1989 - 37^2 - 21^2 = a^2
[?,22,37] : 1989 - 37^2 - 22^2 = a^2
[?,23,37] : 1989 - 37^2 - 23^2 = a^2
[?,24,37] : 1989 - 37^2 - 24^2 = a^2
[?,17,38] : 1989 - 38^2 - 17^2 = a^2
[?,18,38] : 1989 - 38^2 - 18^2 = a^2
[?,19,38] : 1989 - 38^2 - 19^2 = a^2
[?,20,38] : 1989 - 38^2 - 20^2 = a^2
[?,21,38] : 1989 - 38^2 - 21^2 = a^2
[?,22,38] : 1989 - 38^2 - 22^2 = a^2
[?,23,38] : 1989 - 38^2 - 23^2 = a^2
[?,16,39] : 1989 - 39^2 - 16^2 = a^2
[?,17,39] : 1989 - 39^2 - 17^2 = a^2
[?,18,39] : 1989 - 39^2 - 18^2 = a^2
[?,19,39] : 1989 - 39^2 - 19^2 = a^2
[?,20,39] : 1989 - 39^2 - 20^2 = a^2
[?,21,39] : 1989 - 39^2 - 21^2 = a^2
[?,14,40] : 1989 - 40^2 - 14^2 = a^2
[?,15,40] : 1989 - 40^2 - 15^2 = a^2
[?,16,40] : 1989 - 40^2 - 16^2 = a^2
[?,17,40] : 1989 - 40^2 - 17^2 = a^2
[?,18,40] : 1989 - 40^2 - 18^2 = a^2
[?,19,40] : 1989 - 40^2 - 19^2 = a^2
[?,13,41] : 1989 - 41^2 - 13^2 = a^2
[?,14,41] : 1989 - 41^2 - 14^2 = a^2
[?,15,41] : 1989 - 41^2 - 15^2 = a^2
[?,16,41] : 1989 - 41^2 - 16^2 = a^2
[?,17,41] : 1989 - 41^2 - 17^2 = a^2
[?,11,42] : 1989 - 42^2 - 11^2 = a^2
[?,12,42] : 1989 - 42^2 - 12^2 = a^2
[?,13,42] : 1989 - 42^2 - 13^2 = a^2
[?,14,42] : 1989 - 42^2 - 14^2 = a^2
[?,15,42] : 1989 - 42^2 - 15^2 = a^2
[?, 9,43] : 1989 - 43^2 - 9^2 = a^2
[?,10,43] : 1989 - 43^2 - 10^2 = a^2
[?,11,43] : 1989 - 43^2 - 11^2 = a^2
[?, 6,44] : 1989 - 44^2 - 6^2 = a^2
[?, 7,44] : 1989 - 44^2 - 7^2 = a^2
edit - fixing spacing.