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Question Number 151911 by mathdanisur last updated on 24/Aug/21

$$\mathrm{Determine}\mathrm{the}\mathrm{digit}\mathbf{a}\mathrm{and}\mathrm{prime}$$$$\mathrm{numbers}\mathbf{x};\mathbf{y};\mathbf{z}\mathrm{such}\mathrm{that}\mathbf{x}<\mathbf{y},\mathbf{z}<1000$$$$\mathrm{and}\mathrm{x}+{\mathrm{y}}^{2\mathbf{a}}=\mathrm{z}$$

Commented by Rasheed.Sindhi last updated on 24/Aug/21

$$2\mathbf{a}means20,21,22,...,29?Or2\mathbf{a}=2\times \mathbf{a}?$$$${}^{\prime }\mathrm{digit}{\mathbf{a}}^{\prime }meansdecimaldigit?$$

Commented by mathdanisur last updated on 24/Aug/21

$$\mathbf{S}\mathrm{er},2\mathrm{a}=2\mathrm{xa}$$$$\mathrm{a}=0,1,2,3,4,5,6,7,8,9$$$$2\mathrm{a}=2\cdot 2...$$

Commented by mathdanisur last updated on 24/Aug/21

$$\mathrm{Solution}\mathrm{dear}\mathrm{Ser}\mathrm{please}$$

Commented by Rasheed.Sindhi last updated on 24/Aug/21

$$\mathrm{x}+{\mathrm{y}}^{2\mathbf{a}}=\mathrm{z};\mathbf{x}<\mathbf{y},\mathbf{z}<1000;\mathrm{x},\mathrm{y},\mathrm{z}\in \mathbb{P}$$$${}^{\bullet }\mathrm{a}=0:\mathrm{x}+1=\mathrm{z}\Rightarrow \mathrm{x}=2,\mathrm{z}=3\mathrm{\forall }\mathrm{y}(<1000)\in \mathbb{P}$$$$(\mathrm{Two}\mathrm{primes}\mathrm{having}\mathrm{difference}1\mathrm{are}$$$$\mathrm{only}2\mathrm{\&}3)$$$${}^{\bullet }\mathrm{a}=1:2+3^2=11$$

Commented by mathdanisur last updated on 24/Aug/21

$$(x,y,z,a)\in \{(0,2,p,3)(2,3,11,1)(2,3,83,2)$$$$p=prime$$

Commented by MJS_new last updated on 24/Aug/21

$$0\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{prime}\mathrm{number}$$

Commented by mathdanisur last updated on 24/Aug/21

$$\mathrm{in}\mathrm{the}\mathrm{statement}\mathrm{a}\mathrm{is}\mathrm{digit}$$$$\mathrm{i}.\mathrm{e}\mathrm{is}\mathrm{in}\mathrm{the}\mathrm{set}\{0,2,...,9\}$$

Commented by MJS_new last updated on 24/Aug/21

$$(x,y,z,a)\in \{(0,2,p,3)(2,3,11,1)(2,3,83,2)$$$$$$

Commented by MJS_new last updated on 24/Aug/21

$$\mathrm{you}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{seem}\mathrm{to}\mathrm{understand}\mathrm{anything}.$$

Commented by Rasheed.Sindhi last updated on 24/Aug/21

$$(x,y,z,a)\in \left\{(2,p,3,0)(2,3,11,1)(2,3,83,2)\right\}$$

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