Question

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Answer 1

Răspuns:

Vezi atasament

Answer 2

51)

$a = 2000^{15}+2001^{51}+2002^{151}+2003^{41}\\ \\ U(6^n) = 6\\ U(9^{2n}) = 1 \\ \\ U(a) = U\Big(0+1+2^{4\cdot 37+3}+3^{2\cdot20 + 1} }\Big) =U\Big(1+(2^4)^{37}\cdot 2^3+9^{20}\cdot 3\Big) = \\ \\ = U(1+6^{37}\cdot 8+1\cdot 3) = U(1+6\cdot 8+3) = U(1+48+3) = U(52) = 2$

52)

$a = (3^3\cdot 7^5)^2 = 3^{3\cdot 2}\cdot 7^{5\cdot 2} = (3^2)^3+7^{10} = 9^3\cdot 7^{10}\\ b = 9^3\cdot 7^{10} \\ \\ \Rightarrow a-b = 0$