There was a mathematician named Fibonacci who lived in Pisa, in the 13th century. In 1225 he participated in a math contest and there he had to take an exam. He got a problem that requested a very sharp mind and ability for that time and it doesn't seem too easy today either.
Here is the problem: "You should find a perfect square, which should still remain a perfect square even it is increased or decreased with 5."
 

The answer is:

1681/144 or (41/12)*(41/12)
Here is the calculus:
1681/144-5=961/144; 1681/144+5=2401/144
Where:
1681 is square 41
144 is square 12
961 is square 31
2401 is square 49
or:
(41/12)*(41/12)-5=(31/12)*(31/12);
(41/12)*(41/12)+5=(49/12)*(49/12);

Sava Adrian class 9A
"Alexandru Papiu Ilarian" Highschool Dej, Romania
Teacher: Ligia Garlea