Wednesday, May 4, 2011

Digits

202^3 = 8,242,408 = (–8 + 242 – 40 + 8)^3


204 = 3^2 + 7^2 + 5^2 + 11^2 = 2^2 + 8^2 + 6^2 + 10^2,
where 3+7 = 2+8 and after adding 3 to each digit: 6+10 = 5+11.
204^2 = 23^3 + 24^3 + 25^3 = 41,616.


206^3 = 8,741,816 = (8 + 7 + 4 + 181 + 6)^3

208^3 = 8,998,912 = (08 + 99 + 89 + 12)^3

209 = 1^6 + 2^5 + 3^4 + 4^3 + 5^2 + 6^1

305^3 = 28,372,625 = (283 + 7 + 2 + 6 + 2 + 5)^3


494 + 209 = 703 and 494,209 = 703^2


88+209 = 297 and 88,209 = 297^2 and 494+209 = 703 and 494,209 = 703^2 and 297+703 = 1000

2,401 = (2 + 4 + 0 + 1)^4 = 7^4


10,000 = (1+2+3+4)^4 = [(1^5+2^5+3^5+4^5)+(1^7+2^7+3^7+4^7)]/2

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