(In reply to
re: poor explanation by Brian Smith)
So you say that
[(2 + √5)^100 + (2 - √5)^100] is a very big integer (no roots).
Implying that (2 + √5)^100 and (2 - √5)^100 are complementary: if the decimal part of (2 + √5)^100 is r then the decimal part of
(2 - √5)^100 is 1-r
But (2 - √5)^100 is 0,236067^100 and is going to have 61 zeros before the first significative digit. Much more zeros than digits has the expresion (1 + √2)^100 + (1 + √2)^-100 which is the integer (2^51)-1.
Then there are more than 20 zeros to begin the decimal part of
[(2 - √5)^100] * [(1 + √2)^100 + (1 + √2)^-100]
So that there are more than 20 nines to open the decimal part of
[(2 + √5)^100] * [(1 + √2)^100 + (1 + √2)^-100]
Good trick!
Edited on January 28, 2019, 4:30 pm
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Posted by armando
on 2019-01-28 16:26:52 |
re(2): poor explanation
