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Пусть есть три натуральных числа (a,b,c). Построим новую тройку: минимальные натуральные (x,y,z) = g(a,b,c) такие, что
xa=1 mod bc
yb= 1 mod ac
zc=1 mod ab
(а если таких нет, то g не определено)

Эту функцию g можно итерировать, например,
g(3 5 7) = (12 17 13)
g(12 17 13) = (129 101 157)
g(129 101 157) = (1598 8021 6556) и дальше не определено.

Обычно заканчивается за несколько шагов, хотя и очень быстро растёт. Для 3 5 11 довольно долго живёт:

3 5 11
37 20 11
113 346 471
138449 50608 7803
240577745 979838281 3389724067
1418764558193715874 62029164632806621 117103549492669858

Гипотеза: всегда заканчивается за конечное число шагов.



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Пусть есть три натуральных числа (a,b,c). Построим новую тройку: минимальные натуральные (x,y,z) = g(a,b,c) такие, что
xa=1 mod bc
yb= 1 mod ac
zc=1 mod ab
(а если таких нет, то g не определено)

Эту функцию g можно итерировать, например,
g(3 5 7) = (12 17 13)
g(12 17 13) = (129 101 157)
g(129 101 157) = (1598 8021 6556) и дальше не определено.

Обычно заканчивается за несколько шагов, хотя и очень быстро растёт. Для 3 5 11 довольно долго живёт:

3 5 11
37 20 11
113 346 471
138449 50608 7803
240577745 979838281 3389724067
1418764558193715874 62029164632806621 117103549492669858

Гипотеза: всегда заканчивается за конечное число шагов.

BY tropical saint petersburg


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