Перевод числа 999999999999999999999999999 из 999999999999999999999999999999999999999-ой системы счисления в 99999999999999999-ую

Для перевода числа 999999999999999999999999999 из 999999999999999999999999999999999999999-ой в 99999999999999999-ую систему счисления, необходимо сначала перевести его в десятичную систему, а полученное число в 99999999999999999-ую. Для перевода 999999999999999999999999999999999999999-ого числа 999999999999999999999999999 в десятичное необходимо записать его в виде многочлена, состоящего из произведений цифр вида:

A_{999999999999999999999999999999999999999} = a_n-1 ∙ 999999999999999999999999999999999999999^n-1 + a_n-2 ∙ 999999999999999999999999999999999999999^n-2 + ∙∙∙ + a₀ ∙ 999999999999999999999999999999999999999⁰

В результате преобразований получим:

999999999999999999999999999_{999999999999999999999999999999999999999}=9 ∙ 999999999999999999999999999999999999999²⁶ + 9 ∙ 999999999999999999999999999999999999999²⁵ + 9 ∙ 999999999999999999999999999999999999999²⁴ + 9 ∙ 999999999999999999999999999999999999999²³ + 9 ∙ 999999999999999999999999999999999999999²² + 9 ∙ 999999999999999999999999999999999999999²¹ + 9 ∙ 999999999999999999999999999999999999999²⁰ + 9 ∙ 999999999999999999999999999999999999999¹⁹ + 9 ∙ 999999999999999999999999999999999999999¹⁸ + 9 ∙ 999999999999999999999999999999999999999¹⁷ + 9 ∙ 999999999999999999999999999999999999999¹⁶ + 9 ∙ 999999999999999999999999999999999999999¹⁵ + 9 ∙ 999999999999999999999999999999999999999¹⁴ + 9 ∙ 999999999999999999999999999999999999999¹³ + 9 ∙ 999999999999999999999999999999999999999¹² + 9 ∙ 999999999999999999999999999999999999999¹¹ + 9 ∙ 999999999999999999999999999999999999999¹⁰ + 9 ∙ 999999999999999999999999999999999999999⁹ + 9 ∙ 999999999999999999999999999999999999999⁸ + 9 ∙ 999999999999999999999999999999999999999⁷ + 9 ∙ 999999999999999999999999999999999999999⁶ + 9 ∙ 999999999999999999999999999999999999999⁵ + 9 ∙ 999999999999999999999999999999999999999⁴ + 9 ∙ 999999999999999999999999999999999999999³ + 9 ∙ 999999999999999999999999999999999999999² + 9 ∙ 999999999999999999999999999999999999999¹ + 9 ∙ 999999999999999999999999999999999999999⁰ = 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ 1.0E+273 + 9 ∙ 1.0E+234 + 9 ∙ 1.0E+195 + 9 ∙ 1.0E+156 + 9 ∙ 1.0E+117 + 9 ∙ 1.0E+78 + 9 ∙ 1.0E+39 + 9 ∙ 1 = INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + 9.0E+273 + 9.0E+234 + 9.0E+195 + 9.0E+156 + 9.0E+117 + 9.0E+78 + 9.0E+39 + 9 = INF₁₀

Таким образом:

999999999999999999999999999_{999999999999999999999999999999999999999} = INF₁₀.

Для перевода десятичного числа INF в 99999999999999999-ую систему счисления, необходимо его последовательно делить на 99999999999999999 до тех пор, пока остаток не станет меньше чем 99999999999999999.

Ответом будет являться обратная последовательность результатов деления:

0₁₀=0_{99999999999999999}

Окончательный ответ будет выглядеть так:

999999999999999999999999999_{999999999999999999999999999999999999999}=0_{99999999999999999}