How many different triples (a,b,c) from the set {1,2,3,4,5} satisfy the equation a^2 + bc = b^2 + bc?
All these satisfy your equation. Remove any duplicates:
1 = (1, 1, 1)
2 = (2, 2, 1)
3 = (3, 3, 1)
4 = (4, 4, 1)
5 = (5, 5, 1)
6 = (1, 1, 2)
7 = (2, 2, 2)
8 = (3, 3, 2)
9 = (4, 4, 2)
10 = (5, 5, 2)
11 = (1, 1, 3)
12 = (2, 2, 3)
13 = (3, 3, 3)
14 = (4, 4, 3)
15 = (5, 5, 3)
16 = (1, 1, 4)
17 = (2, 2, 4)
18 = (3, 3, 4)
19 = (4, 4, 4)
20 = (5, 5, 4)
21 = (1, 1, 5)
22 = (2, 2, 5)
23 = (3, 3, 5)
24 = (4, 4, 5)
25 = (5, 5, 5)
+117437 How many different triples (a,b,c) from the set {1,2,3,4,5} satisfy the equation a^2 + bc = b^2 + bc
a^2 + bc = b^2 + bc
a^2 = b^2
since there are no negative choices, a=b c can be any number
If numbers cannot be reused then there are no solutions
if numbers can be reused then there are 5*5=25 triplets
