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Question Number 18949 by Tinkutara last updated on 01/Aug/17

$$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{numbers}⩽{10}^8$$$$\mathrm{which}\mathrm{are}\mathrm{neither}\mathrm{perfect}\mathrm{squares},\mathrm{nor}$$$$\mathrm{perfect}\mathrm{cubes},\mathrm{nor}\mathrm{perfect}\mathrm{fifth}\mathrm{powers}.$$

Commented by prakash jain last updated on 03/Aug/17

$$\mathrm{i}\mathrm{retyped}\mathrm{the}\mathrm{answer}.$$

Answered by prakash jain last updated on 03/Aug/17

$$\mathrm{no}\mathrm{of}\mathrm{perfect}\mathrm{squares}={10}^4$$$$\mathrm{no}\mathrm{of}\mathrm{perfect}\mathrm{cubes}=464$$$$\mathrm{no}\mathrm{of}\mathrm{perfect}\mathrm{power}5=39$$$$\mathrm{no}\mathrm{of}\mathrm{perfect}\mathrm{power}6=21$$$$\mathrm{no}\mathrm{of}\mathrm{perfect}\mathrm{power}15=3$$$$\mathrm{no}\mathrm{of}\mathrm{perfect}\mathrm{power}10=6$$$$\mathrm{no}\mathrm{of}\mathrm{perfect}\mathrm{power}30=1$$$$\mathrm{number}\mathrm{of}\mathrm{perfect}\mathrm{squares}$$$$\mathrm{cubes}\mathrm{and}\mathrm{power}5$$$$\mathrm{n}=10000+464+39-21-3-6+1$$$$\mathrm{requited}\mathrm{answer}={10}^8-\mathrm{n}$$

Commented by Tinkutara last updated on 03/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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