Question

determinati cifrele nenule a si b in baza 10, astfel incat nr nat n=aaa-abb+3(b-a)sa fie patrat perfect

Answer 1

n= 100 a +10 a +a - 100 a - 10 b - b +3 b- 3 a
n=11 a - 11 b +3 b - 3 a
n= 8 a - 8 b
n= 8 (a-b) ⇒ n= 2³ * (a-b) patrat perfect ⇒ a-b=2 ⇒ a = b+2

(a;b) ∈ {(3;1) ; (4;2) ; (5;3); (6;4); (7;5) ; (8;6); (9;7)}