2016年12月6日 · 3 % 7 = 3 How? Well we know that modulo returns the remainder. 3 / 7 = 0.428 means the highest number that can be multiplied by 7 to get 3 or a value close to 3 is 0. 0 …

For example, $0\equiv 7\mod 7$, but the values $3^0 \equiv 1$ and $3^7 \equiv 3$ are not identical mod $7$. $\endgroup$ – azimut Commented Feb 11, 2013 at 18:32

2012年10月8日 · The inverse of 4 mod 7 = ? First note that gcd(4, 7) = 1. Look at multiples of 7, add 1, and scan that list for divisibility by 4: Multiples of 7: 0, 7, 14, 21 Multiples of 7, then +1 …

Sorry this is a really simple problem but I couldnt figure it out. I'm trying to find the value of $3^{1000}\\bmod 7$. I know the actual value is 4, but I used a calculator. How would I simplify …

Your observation is very close to the key idea: the reason that the proof works is the following. If $\rm\,k\equiv 1\pmod 3\,$ and $\rm\,k\equiv 0\pmod 2\,$ then $\rm\,k^n \equiv k\,$ holds both …

$\begingroup$ @YoTengoUnLCD It is not easy to make that precise before one learns about localizations. Informally, it is true because such fraction arithmetic uses only the ring axioms …

2013年7月8日 · Modulus operator gives you the result in 'reduced residue system'. For example for mod 5 there are 5 integers counted: 0,1,2,3,4. In fact 19=12=5=-2=-9 (mod 7). The main …

2017年10月9日 · $\begingroup$ Note that the inverse of $30$ is not $3$, but rather $-3$ from what you have written, since $30 \times -3 \equiv 1 \mod 7$ from above. $\endgroup$ – …

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2013年2月28日 · These emphasized points are all $\equiv 0\text{ mod } 7$. You can see that -10 is 4 points to the right of $-2\times7$. It's also 3 points to the left of $-1\times7$. Since -10 is …