Euler's theorem
calccrypto 1246373018|%e %b %Y, %H:%M %Z|agohover
(1)
can someone tell me why this part is true?
(2)how does the 7^4 come out?
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Euler's theorem
Started by: calccrypto
On: 1246373018|%e %b %Y, %H:%M %Z|agohover
Number of posts: 13
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calccryptoOn: 1246373018|%e %b %Y, %H:%M %Z|agohover
Number of posts: 13
RSS: New posts
calccrypto 1246373018|%e %b %Y, %H:%M %Z|agohover
Re: Euler's theorem
DarkerLine 1246375687|%e %b %Y, %H:%M %Z|agohover
is actually the meat of Euler's theorem, since 4 is φ(10). This means that whenever 74 occurs in an equivalence mod 10, we can substitute 1 for it: if 
, then 
(raising both sides to a power), and 
(multiplying both sides by 72).
Another way to see it is this: taking things mod 10 is equivalent to finding the last digit of a number. When multiplying two large numbers (e.g. 74*72 = 2401*49), if all we care about is the last digit of the result, we don't need to know what the other digits of the numbers themselves are, so we might as well just multiply 1*9. This is exactly what we're doing here: the last digit of 74 is 1, so we replace 74 by 1 when doing a last-digit calculation.
Re: Euler's theorem
calccrypto 1246400339|%e %b %Y, %H:%M %Z|agohover
so because 10 has 4 values comprime to it we can substitute 1 for it:?
¿¿¿que???
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Re: Euler's theorem
graphmastur 1246401400|%e %b %Y, %H:%M %Z|agohover
Actually, when you ask someone "what" in spanish, as in what did you say, or what was that, you actually do Cómo.
As for the problem, I have no earthly idea. Power wise, the 7 to the 4th to the 55th, is 7 to the 59th. However, he said that 7 to the 4th is equal to 1, so I don't know.
"But sanctify the Lord God in your hearts, and always be ready to give a defense to everyone who asks you a reason for the hope that is in you, with meekness and fear;" ~ 1 Peter 3:15
Re: Euler's theorem
Weregoose 1246405079|%e %b %Y, %H:%M %Z|agohover
Modular arithmetic would be very useful knowledge, so you should read up on it. …Imagine a clock face with ten hours. Starting at 0:00/10:00, we then move forward 7^4 hours. What hour would that be?
Also, you might remember that the last digit of a number can be acquired with 10fPart(.1X). This immediately follows from 10fPart(X/10), which can act as a replacement for X-10int(X/10) – essentially, we're using X (mod 10).
Re: Euler's theorem
calccrypto 1246410799|%e %b %Y, %H:%M %Z|agohover
yeah. i know that much, i think. the clock would be 7^4 mod 10, but no further
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Re: Euler's theorem
Timothy Foster 1246411149|%e %b %Y, %H:%M %Z|agohover
@graphmastur (74)55 = 7220 since (xa)b = xab.
If you multiplied to numbers of the same base, then you add the exponents. xa*xb = xa+b
— Blog ~ Life's Handbook
Re: Euler's theorem
graphmastur 1246413419|%e %b %Y, %H:%M %Z|agohover
Right, and (X^a)^b = X^(a*b).
I just couldn't understand how 7^4 = 1.
"But sanctify the Lord God in your hearts, and always be ready to give a defense to everyone who asks you a reason for the hope that is in you, with meekness and fear;" ~ 1 Peter 3:15
Re: Euler's theorem
Timothy Foster 1246421284|%e %b %Y, %H:%M %Z|agohover
I have never seen modular arithmetic before, but it seems to imply the elementary idea of remainders in division. For example, you can say that (although it is misleading and simply not mathematically proper) 17/4 is 4 with a remainder of 1. Therefore, 17 mod 4 is 1. I do not have any idea if this is entirely correct. Upon research, it seems there is more to this than what I hypothesize.
In mod 10, this is easy. The equivalence is simply the last digit of the integer. 134 = 4 mod 10. Therefore, 74 = 2401, which in mod 10 is 1. This is how this equivalence is made above.
— Blog ~ Life's Handbook
Re: Euler's theorem
calccrypto 1246417128|%e %b %Y, %H:%M %Z|agohover
yeah. i always failed at spanish. thank goodness im finished with it though
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Re: Euler's theorem
calccrypto 1246417315|%e %b %Y, %H:%M %Z|agohover
what do you mean "occurs in an equivalence"?
and how would your explanation work with other numbers? im horribly inept at substitution for some reason
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Re: Euler's theorem
DarkerLine 1246484945|%e %b %Y, %H:%M %Z|agohover
What I mean is that 74 obviously isn't equal to 1 — it's only equivalent to 1 mod 10. So you can substitute 1 for it, but only when you're working in mod 10.
Re: Euler's theorem
calccrypto 1246486812|%e %b %Y, %H:%M %Z|agohover
ah. i see now
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