Question

Determinati cifrele nenule a si b in baza 10 astfel incat numarul natural; n=aaa-abb+3(b-a) sa fie patrat perfect

Answer 1

n=111a-100a-11b+3b-3a
n=8a-8b
n=8(a-b)
n patrat perfect=>
a-b=2 sau 8
1)a=b+2
b=1=>a=3
b=2=>a=4
b=3=>a=5
b=4=>a=6
b=5=>a=7
b=6=>a=8
b=7=>a=9

2)a=b+8
b=1=>a=9