Question

Докажите, что: 5^7-5^6+5^5 делится на 21 2^18-2^17+2^16-2^15 делится на 15

Answer 1

$\frac{5^7-5^6+5^5}{21} = \frac{5^5(5^2-5^1+1)}{21} =\frac{5^5(25-5+1)}{21} =\frac{5^5*21}{21} =5^5=3125$

$\frac{2^{18}-2^{17}+2^{16}-2^{15}}{15} = \frac{2^{15}(2^3-2^2+2^1-1)}{15} =\frac{2^{15}(8-4+2-1)}{15} = \\ \\ =\frac{2^{15}*5}{15} = \frac{2^{15}}{3} = \frac{32768}{3} =10922 \frac{2}{3}$