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Question Number 5152 by 1771727373 last updated on 23/Apr/16

$$thereisaninetergera,b,c$$$$cantherebeanintergeras$$$$a^n+b^{n+1}=c^{n+2}\left(nisainterger\right)$$$$$$

Commented by Yozzii last updated on 25/Apr/16

$$Letn=0\Rightarrow 1+b=c^2$$$$Let(a,b,c)=(0,8,3)$$$$\Rightarrow 1+8=3^2\Rightarrow 9=9.$$

Commented by Rasheed Soomro last updated on 06/May/16

$$\mathrm{If}(a,b,c)=(0,8,3)\mathrm{then}\mathrm{for}\mathrm{n}=0$$$$a^n+b^{n+1}=c^{n+2}\Rightarrow 0^0+8^1=3^2$$$$\mathrm{Does}{0}^0=1?$$$$\mathrm{I}\mathrm{think}{0}^0\mathrm{is}\mathrm{indeterminate}\mathrm{and}$$$$\mathrm{a}\mathrm{is}\mathrm{an}\mathrm{integer}\mathrm{other}\mathrm{than}0.$$

Commented by prakash jain last updated on 08/May/16

$$0^0\mathrm{is}\mathrm{indeteminate}\mathrm{only}\mathrm{when}\mathrm{it}\mathrm{occurs}\mathrm{as}$$$$\mathrm{a}\mathrm{limit}\mathrm{in}\mathrm{that}\mathrm{case}\mathrm{that}\mathrm{value}\mathrm{of}\mathrm{limits}$$$$\mathrm{depends}\mathrm{on}\mathrm{the}\mathrm{function},\mathrm{in}\mathrm{this}\mathrm{case}$$$$\underset{a\to 0}{\lim }{a}^0=1$$

Commented by Rasheed Soomro last updated on 08/May/16

$$\mathrm{This}\mathrm{is}\mathrm{knowledge}\mathrm{for}\mathrm{me}.\mathrm{Thanks}!$$

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