Question

Scrieți nr 65^2001 ca o sumă de 2 pătrate perfecte în 2 moduri.
Sunt in cls a 5 a
Va rog frumos sa ma ajutati !!!!!

Answer 1

Varianta 1:

65^2001 = 65 × 65^2000 = (1+64)× 65^2000 = 1 × 65^2000 + 64 × 65^2000 = (65^1000)^2 + (8×65^1000)^2

Varianta 2:

65^2001 = (5×13)^2001 = 5^3 × 5^1998 × 13 × 13^2000 = (125×13)×(5^1998×13^2000) = 1625 × (5^1998×13^2000) = (256 + 1369) × (5^1998×13^2000) = 16^2 × (5^999)^2 × (13^1000)^2 + 37^2 × (5^999)^2 × (13^1000)^2 = (16×5^999×13^1000)^2 + (37×5^999×13^1000)^2