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A Poetry of Numbers

3+24=27 \to 3 \cdot 24=72

2+47=49 \to 2 \cdot 47=94

2+497=499 \to 2 \cdot 497=994

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512=(5+1+2)^3=8^3

19,683=(1+9+6+8+3)^3=27^3

205,962,976=(2+0+5+9+6+2+9+7+6)^5=46^5

248,155,780,267,521=(2+4+8+1+5+5+7+8+0+2+6+7+5+2+1)^8=63^8

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153 = 1^3 + 5^3 + 3^3 = 1+125+27

371 = 3^3 + 7^3 + 1^3 = 27+343+1

407 = 4^3 + 0^3 + 7^3 = 64+0+343

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175 = 1^1 + 7^2 + 5^3 = 1+49+125

598 = 5^1 + 9^2 + 8^3 = 5+81+512

1,676 = 1^1 + 6^2 + 7^3 + 6^4 = 1+36+343+1,296

2,427 = 2^1 + 4^2 + 2^3 +7^4 = 2+16+8+2,401

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3,435 = 3^3 + 4^4 + 3^3 + 5^5

438,579,088 = 4^4 + 3^3 + 8^8 + 5^5 + 7^7 + 9^9 + 0 + 8^8 + 8^8

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15 = 1^1 + 6^1 + 8^1 = 2^1 + 4^1 + 9^1

101 = 1^2 + 6^2 + 8^2 = 2^2 + 4^2 + 9^2

26 = 1^1 + 5^1 + 8^1 + 12^1 = 2^1 + 3^1 + 10^1 +11^1

234 = 1^2 + 5^2 + 8^2 + 12^2 = 2^2 + 3^2 + 10^2 +11^2

2,366 = 1^3 + 5^3 + 8^3 + 12^3 = 2^3 + 3^3 + 10^3 +11^3

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6,205 = 38^2 + 69^2 \leftrightarrow 3,869 = 62^2 + 05^2

7,706 = 59^2 + 65^2 \leftrightarrow 5,965 = 77^2 + 06^2

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352  \to 3^3 + 5^3 + 2^3 = 27+125+8=160

160 \to 1^3 + 6^3 + 0^3 =1+216+0=217

217 \to 2^3 + 1^3 + 7^3 = 8+1+343= 352

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145 = 1! + 4! + 5! = 1+24+120

40,585 = 4! + 0! + 5! + 8! + 5! = 24+1+120+40,320+120

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872  \to 8! + 7! + 2! = 40,320+5,040+2 = 45,362

45,362 \to 4! + 5! + 3! + 6! + 2! = 24+120+6+720+2 = 872

169  \to 1! + 6! + 9! = 1+720+36,2880 = 36,3601

36,3601 \to 3! + 6! + 3! + 6! + 0! + 1! = 6+24+6+24+1+1 = 1,454

1,454 \to 1! + 4! + 5! + 4! = 1+24+120+24 = 169

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