Перевод числа 9999999999999999999999999999999999 из 99999999999999999999999999-ой системы счисления в 999999999999999999999999-ую

Для перевода числа 9999999999999999999999999999999999 из 99999999999999999999999999-ой в 999999999999999999999999-ую систему счисления, необходимо сначала перевести его в десятичную систему, а полученное число в 999999999999999999999999-ую. Для перевода 99999999999999999999999999-ого числа 9999999999999999999999999999999999 в десятичное необходимо записать его в виде многочлена, состоящего из произведений цифр вида:

A_{99999999999999999999999999} = a_n-1 ∙ 99999999999999999999999999^n-1 + a_n-2 ∙ 99999999999999999999999999^n-2 + ∙∙∙ + a₀ ∙ 99999999999999999999999999⁰

В результате преобразований получим:

9999999999999999999999999999999999_{99999999999999999999999999}=9 ∙ 99999999999999999999999999³³ + 9 ∙ 99999999999999999999999999³² + 9 ∙ 99999999999999999999999999³¹ + 9 ∙ 99999999999999999999999999³⁰ + 9 ∙ 99999999999999999999999999²⁹ + 9 ∙ 99999999999999999999999999²⁸ + 9 ∙ 99999999999999999999999999²⁷ + 9 ∙ 99999999999999999999999999²⁶ + 9 ∙ 99999999999999999999999999²⁵ + 9 ∙ 99999999999999999999999999²⁴ + 9 ∙ 99999999999999999999999999²³ + 9 ∙ 99999999999999999999999999²² + 9 ∙ 99999999999999999999999999²¹ + 9 ∙ 99999999999999999999999999²⁰ + 9 ∙ 99999999999999999999999999¹⁹ + 9 ∙ 99999999999999999999999999¹⁸ + 9 ∙ 99999999999999999999999999¹⁷ + 9 ∙ 99999999999999999999999999¹⁶ + 9 ∙ 99999999999999999999999999¹⁵ + 9 ∙ 99999999999999999999999999¹⁴ + 9 ∙ 99999999999999999999999999¹³ + 9 ∙ 99999999999999999999999999¹² + 9 ∙ 99999999999999999999999999¹¹ + 9 ∙ 99999999999999999999999999¹⁰ + 9 ∙ 99999999999999999999999999⁹ + 9 ∙ 99999999999999999999999999⁸ + 9 ∙ 99999999999999999999999999⁷ + 9 ∙ 99999999999999999999999999⁶ + 9 ∙ 99999999999999999999999999⁵ + 9 ∙ 99999999999999999999999999⁴ + 9 ∙ 99999999999999999999999999³ + 9 ∙ 99999999999999999999999999² + 9 ∙ 99999999999999999999999999¹ + 9 ∙ 99999999999999999999999999⁰ = 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 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ 1.0E+286 + 9 ∙ 1.0E+260 + 9 ∙ 1.0E+234 + 9 ∙ 1.0E+208 + 9 ∙ 1.0E+182 + 9 ∙ 1.0E+156 + 9 ∙ 1.0E+130 + 9 ∙ 1.0E+104 + 9 ∙ 1.0E+78 + 9 ∙ 1.0E+52 + 9 ∙ 1.0E+26 + 9 ∙ 1 = INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + 9.0E+286 + 9.0E+260 + 9.0E+234 + 9.0E+208 + 9.0E+182 + 9.0E+156 + 9.0E+130 + 9.0E+104 + 9.0E+78 + 9.0E+52 + 9.0E+26 + 9 = INF₁₀

Таким образом:

9999999999999999999999999999999999_{99999999999999999999999999} = INF₁₀.

Для перевода десятичного числа INF в 999999999999999999999999-ую систему счисления, необходимо его последовательно делить на 999999999999999999999999 до тех пор, пока остаток не станет меньше чем 999999999999999999999999.

Ответом будет являться обратная последовательность результатов деления:

0₁₀=0_{999999999999999999999999}

Окончательный ответ будет выглядеть так:

9999999999999999999999999999999999_{99999999999999999999999999}=0_{999999999999999999999999}