The ≡ sign can be read as "is equivalent to"
10^101 ≡ 3^101 when divided by 7
3^101 = (3²)⁵⁰.3 ≡ 2⁵⁰.3 (because 3² = 9 ≡ 2)
2⁵⁰.3 = (2³)¹⁶.2².3 ≡(1)¹⁶.4.3 = 12 (because 2³ = 8 ≡ 1)
12 ≡ 5 on div. by 7
So 2^101 is a very large number of whole weeks and 5 extra days.
4/25/07 was a Wednesday. 5 days later is a Monday.
So the day will be a Monday.
2007-04-28 06:22:00
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answer #1
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answered by sumzrfun 3
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Well,let's see. 4/25/07 was on a Wednesday.
If we advance 7 days we end up on the same
day.
So all we need to do is find 10^101 mod 7.
Now 7 divides 1001, so 10^3 = 6(mod 7)
and 10^ 6 = 1(mod 7)
So 10^ 101 = 10^96 * 10^5(mod 7) = 10^5(mod 7).
= 10^6/10 = 1/10 = 5( mod 7).
So 10^101 days from now it will be Monday.
Only problem I have here is,
will the earth still be here 10^101 days from now??
The earth is only expected to last about another
4 billion years, which is far less than 10^101 days!
2007-04-28 13:18:27
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answer #2
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answered by steiner1745 7
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I can't give you the definite answer since I don't have a supercalculator with me, but here's how you'd find it:
take the number 10^101, and then through trial and error, find the greatest amount of the number 7 that can fit into 10^101. in other words, divide 10^101 by 7 but don't find the remainder, and then multiply seven by the quotient. then subtract that number from 10^101, and you should have an answer that's anywhere between 0 and 6.
now, 4/25/07 was a wednesday, so if your number is 0, then the day of the week in the future will be wednesday. if it's 1, then tuesday. and so on.
2007-04-28 13:11:47
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answer #3
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answered by car of boat 4
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What you are essentially asking is to find n such that n=10^101 mod 7
Fermat's little theorem says that for any integer a and any prime p,
a^p=a mod p and
a^(p-1)=1 mod p
Let a=10 and p=7
10^6 = 1 mod 7
(10^6)^16=10^96=1 mod 7
10^101=10^5*10^96
10^101=10^5 mod 7
10^5 mod 7=5 (100,000/7=14286 5/7)
So if April 25 was on a Wednesday, 10^101 days later would be 5 days later in the week, or Monday.
2007-04-28 13:41:46
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answer #4
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answered by Astral Walker 7
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Since the day of the week is a human construct, and we'll all be toast before the sun even gets to the red giant stage, does it really matter? Also the calender has changed over history, so the answer could well be wrong even if I could remember how to calculate it.
2007-04-28 13:17:19
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answer #5
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answered by tinkertailorcandlestickmaker 7
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