Question

Doy 55 puntos por esta par de preguntas

Answer 1

En la primera pregunta hay un error. Propondré corregirla de la siguiente forma

$\text{Hallar el resto de dividir }\underbrace{3535...35}_{64~cifras}\text{ entre 11}\\ \\\textbf{Soluci\'on}\\\\\underbrace{3535...35}_{64~cifras}=35\times\underbrace{1010...101}_{64~cifras}\\\\\underbrace{3535...35}_{64~cifras}=35\times(1+10^2+10^4+10^6+...+10^{62})\\\\...\\10\equiv -1 \mod 11\\35\equiv 2\mod 11...\\\\\underbrace{3535...35}_{64~cifras}\equiv 2\times(1+(-1)^2+...+(-1)^{62}) \mod 11$

$\underbrace{3535...35}_{64~cifras}\equiv 2(63)\mod 11\\\\\underbrace{3535...35}_{64~cifras}\equiv 2(-3)\mod 11\\\\\underbrace{3535...35}_{64~cifras}\equiv -6\mod 11\\\\\underbrace{3535...35}_{64~cifras}\equiv 5\mod 11$

Así el residuo de dividir es 5.

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$4530 + a = 8k\\8k'+2 + a = 8k\\a= 8k''-2\\a=6\\==========================\\\overline{7x6x}=9r\\7+x+6+x=9r\\2x+13=9r\\2x=9r'-4\\x=9r''-2\\\\\boxed{x=7}$

Answer 2

Respuesta:

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