Fus Ro Dah
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Digits. (1 Viewer)
- Thread starter Fus Ro Dah
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deswa1
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Yay- this is actually a question that I know how to do lol (like the first one you've ever posted haha). I'll post a solution when I get back from lunch unless if someone else has done it sooner
RealiseNothing
what is that?It is Cowpea
The last two digits of powers of 7 cycle between 01, 07, 49, and 43.
The third digit is multiplied by 7 for 01 and 07, and is multiplied by 7 plus 3 for 49 and 43. Since you start off with the third digit being 0 (
) you get:
 + 3) \times 7) + 3)
And this pattern repeats. The third digit goes in a cycle of 20 digits:
0 0 0 3 4 8 6 5 8 6 2 7 2 4 8 9 6 2 4 1
Now it starts at
So we want the 10,000th digit in this cycle. Which is the last digit since there are 20 digits in the cycle, which divides 10,000.
Hence the last 3 digits are 143.
The third digit is multiplied by 7 for 01 and 07, and is multiplied by 7 plus 3 for 49 and 43. Since you start off with the third digit being 0 (
And this pattern repeats. The third digit goes in a cycle of 20 digits:
0 0 0 3 4 8 6 5 8 6 2 7 2 4 8 9 6 2 4 1
Now it starts at
Hence the last 3 digits are 143.
