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klio [65]
3 years ago
5

Please help me with this math

Mathematics
1 answer:
s2008m [1.1K]3 years ago
4 0
Ur screwed lol good luck
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Calculate gcd(77, 30) by using the Euclidean algorithm. Find also integers u and v such that 49u + 30v = 1. Furthermore, find su
VladimirAG [237]

Answer:

1. gcd(77,30)=1

77=2*30+17\\30=1*17+13\\17=1*13+4\\13=3*4+1\\4=4*1+0

Since 1 is the last non zero remainder appearing in these equations then, 1 is the gcd of 77 and 30.

2. u=-11, v=18

Using the Euclidean Algorithm we have that

49=1*30+19\\30=1*19+11\\19=1*11+8\\11=1*8+3\\8=2*3+2\\3=1*2+1\\2=1*2+0

Now, we express the remainder as linear combinations of 49 and 30.

1&=3-2\\ &=3-(8-2*3)=3-8+2*3\\&=(11-8)-8+2(11-8)=3*11-4*8\\&=3*11-4(19-11)=7*11-4*19\\&=7(30-19)-4*19=7*30-11*19\\&=7*30-11(49-30)=\\&=18*30-11*49

Then 1=(-11)49+18*30

3. x=18

If 30x\equiv 1\text{mod 77} then

30x=k*77+1 for some k\in \mathbb{Z}.

Then, if k=7,

30x=7*77+1=540\\x=\frac{540}{30}=18

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3 years ago
Help with number one please and thank youuu
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I believe its D

Step-by-step explanation:

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