Find the inverse for 43 modulo 660

Question

03-07-2017
Mathematics

contestada

Find the inverse for 43 modulo 660

Respuesta :

Otras preguntas

Migration, hibernation, and dormancy are all methods of A. producing food B. changing the environment C. adapting to changes in the environment D. producing en

A restaurant owner needs to order at least 176 filet mignon steaks to be stocked for a busy Friday night. He only has room to store 321 steaks in his refrigerat

Which Is the answer ??

Iii. Complete each sentence by following the instruction in brackets.1. The children sailed paper boats____________________________________ (add prepositional p

Select all tables thaf represent A proportional relationship between x and y. A: X: 0, 1, 2, 3 Y: 3, 6, 9, 12 B: X: 2, 3, 4, 5 Y: 12, 18, 2

All the following statements about uncontrolled cellular division are true EXCEPT A. Produce tumors B. Crowd out the healthy tissue C. Are not caused by mutatio

write the expression/equation for each of these statements, don't answer the equation. no need to use units

a number plus 6 is greater than 1

Please helppppppppppp

Oranges sell for $5.00 per bag. If the bag weighs 2 pounds, how much is the price per pound? A $10.00 per pound B $1.50 per pound C $2.50 per pound D $0.50

LammettHash LammettHash · Answer 1 · 2017-07-05T20:24:51+02:00

We're looking for [tex]x[/tex] such that

[tex]43x\equiv1\mod{660}[/tex]

so for some integer [tex]n[/tex] we can write

[tex]43x+660n=1[/tex]

Apply Euclid's algorithm:

[tex]660=43(15)+15[/tex]
[tex]43=15(2)+13[/tex]
[tex]15=13(1)+2[/tex]
[tex]13=2(6)+1[/tex]
[tex]\implies(660,43)=(43,15)=(15,13)=(13,2)=1[/tex]

From this we have

[tex]1=13-2(6)[/tex]
[tex]\implies1=-6(15)+7(13)[/tex]
[tex]\implies1=-20(15)+7(43)[/tex]
[tex]\implies1=-20(660)+307(43)[/tex]
[tex]\implies(-20(660)+307(43))\equiv307(43)\equiv1\mod{660}[/tex]

which means 307 is the inverse of 43 modulo 660.