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Fill in the gags. there an was old the forest. tree it. sam and kate to the door. they went rte temple. they climbed some rocks. there was a picture the wall. the girl the picture had an orchid her hand. zack and tex were the temple. they closed the door and put some rocks it. kate and sam were treat temple.

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78! +79! =78! +78! \cdot 79=78! (1+79)=78! \cdot 80

по свойству степеней 10^n=(2\cdot 5)^n=2^n\cdot 5^n и 2,5, - простые.

подсчитаем сколько раз входит число 2 в факториал 78

s=[\dfrac{78}{2}]+[\dfrac{78}{4}]+[\dfrac{78}{8}]+[\dfrac{78}{16}]+[\dfrac{78}{32}]+[\dfrac{78}{64}]=39+19+9+4+2+1=74

то есть, в числе 78! двойка встречается 74 раза.

подсчитаем сколько раз входит число 5 в факториал 78

s=[\dfrac{78}{5}]+[\dfrac{78}{25}]=15+3=18

в числе 78! пятерка встречается 18 раз.

таким образом, 78! \cdot 80=5^{18}\cdot 2^{74}\cdot a\cdot 8\cdot 10=10^{19}\cdot a

\max (n)=19   — ответ


In next to up ? on to on on in in next to ?

Fill in the gags.there was an old building in the forest.trees grew in  it.sam and kate climbed up the temble.they climbed over some rocks.there was a picture on the wall.the girl on  the picture had an orchids in   her hand.zack and tex were behind  the temble.they closed the door and put some rocks outside it.kate and sam were inside the temble.

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