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To find what number modulo n n this fraction represents, you need to evaluate b−1 b − 1. You can do that by using the Euclidean algorithm to solve the Bézout equation bx + ny = 1 b x + n y = 1. The x x in this equation will give you b−1 b − 1. If you know the factorization of n n you can also use Euler's totient function by noting that ...
You already know what 439 is mod 713. What is $439^2 \mod 713$? What about $439^4$? (Hint: take your answer for $439^2$ after reducing it mod 713, and then square it again.) In the same way, calculate $439^8, 439^{16}, \dots, 439^{128} \mod 713$. Now just note that 233 = 128 + 64 + 32 + 8 + 1.
6. There are ways to calculate it, modulo is remainder counting basically. 7 = 2 mod 5 because 7 = 5 ∗ 1 + 2 12 = 2 mod5 because 12 = 5 ∗ 2 + 2 and so on, so if you want to calculate for example 73 = a mod 7 you can do this, that is want to get a, take 73 and continue subtracting 7 until you no longer can. 73 − 7 = 66, 66 − 7 = 59 etc ...
41mod5 41 m o d 5. 1) I start by dividing the number by the modulus. 41/5 = 8.2 41 / 5 = 8.2. 2)Remove the integer part of the answer. 0.2 0.2. 3) Multiply by the modulus. 0.2 ∗ 5 = 1 0.2 ∗ 5 = 1. This method works great for small modulus calculations, but I can't wrap my head around how to do it with bigger numbers since I can't get the ...
1. By definition of modular arithmetic, 3524 (mod 63) is the remainder when 3524 is divided by 63. To find − 3524 (mod 63), multiply your answer for 3524 (mod 63) by − 1. If you want a positive residue, add 63 to this result. For the product 101 ⋅ 98 mod17, use the theorem that if a ≡ b (mod n) and c ≡ d (modn), then ac ≡ bd (mod n).
Therefore 31 = 7 ⋅ 4 + some number 31 = 7 ⋅ 4 + some number, where your goal is to determine what some number some number is. This same exact process applies for negative numbers. If you want to evaluate −11 (mod 7) − 11 (mod 7), you need the largest multiple of 7 7 that's less than or equal to −11 − 11. This is −14 − 14.
There is a mod function in TI NSpire and any graphing calculator: Syntax: mod (number to divide, modulus (divisor)) E.g. mod (35^51, 319) Enter yields 167. Share. Cite. answered Jul 13, 2016 at 13:48. Alik Z. 11 1. Add a comment.
8. We can use the Chinese remainder theorem. Let (Big Number) = x (Big Number) = x. Notice that x ≡ 0 (mod 9) x ≡ 0 (mod 9) since each factor is divisible by 3 3, and further x ≡ 1 (mod 2) x ≡ 1 (mod 2) since it is a product of two odd numbers. We have gcd(2, 9) = 1 gcd (2, 9) = 1 and 18 = 2 × 9 18 = 2 × 9, so the theorem guarantees a ...
I've read about Fermat's little theorem and generally how congruence works. But I can't figure out how to work out these two: $13^{100} \\bmod 7$ $7^{100} \\bmod 13$ I've also heard of the Congruence
8126=8100+27-1. Notice how 8100 and 27 are multiples of 9. The sum, 8127, is also a multiple of 9, which signifies that 8127 mod 9=0. In modular arithmetic , 0-1=8, so 8126 mod 9=8. (Notice: If you are still confused, draw a circle and draw nine points, writing the numbers 0-8 on the dots clockwise. Now, go to point 0 and go one point ...