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#### Arithmetics. Mental maths

Carpenters were sawing some logs. They made 10 cuts and this produced 16 pieces of wood. How many logs did they saw?

#### Integer and fractional parts. Archimedean property

Are there such irrational numbers $a$ and $b$ so that $a > 1,\, b > 1,$ and [$a^m$] is different from [$b^n$] for any natural numbers $m$ and $n$?

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