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сладко стянул
а теперь панчлайн: биномиальные коэффициенты (как функции от верхнего индекса) периодичны по любому модулю. Вот и получается периодичность g_k.
Панчлайн доказывается так: сразу можно считать, что n=N, зафиксировать m, и доказывать индукцией по N. При N=0,1 понятно. Переход от N к N+1 — см. картинку.

Не знаю, можно ли уменьшить период, не сильно усложнив доказательство



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Панчлайн доказывается так: сразу можно считать, что n=N, зафиксировать m, и доказывать индукцией по N. При N=0,1 понятно. Переход от N к N+1 — см. картинку.

Не знаю, можно ли уменьшить период, не сильно усложнив доказательство

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