Question

aratati ca nr. 13^2=12^2+5^2 si folosind eventual egalitate,demonstrati ca 13^100 se poate scrie ca o suma de doua patrate ale unor nr. nat.

Answer 1

$13^{2} =12^{2} +5^{2} \\169 = 144+25 \\169 = 169\\\\13^{100}= x^{2} +y^{2}\\(13^{2})^{50}=(12^{2} +5^{2})^{50}\\169^{50}=169^{50}$