Hi,
Just need help with a couple of Q's.
Using Euclids algorithm, find:
3568a = 1 mod 1127
and
Use Euclids algorithm to find x and y so 6804x +1343y = 1
Ty for any help.
Read about Bezout's Identity: I'll do (2) and that must suffice to do (1):
$\displaystyle 6804 = 5\cdot 1343+89$ --- first line
$\displaystyle 1343=15\cdot 89+8$ --- second line
$\displaystyle 89=11\cdot 8+1$ --- third line
$\displaystyle 8=8\cdot 1$ --- fourth and final line
Now begin from one line before the end upwards, writing each time the remainder as a combination of the other two elements:
$\displaystyle 1=89-11\cdot 8$ --- from 3rd line
$\displaystyle 1=89-11\cdot 8=89-11(1343-15\cdot 89)=166\cdot 89-11\cdot 1343$ --- from 2nd line
$\displaystyle 1=166\cdot 89-11\cdot 1343=166(6804-5\cdot 1343)-11\cdot 1343=166\cdot 6804 -841\cdot 1343$ --- from 1st line
And voila!: $\displaystyle 1=166\cdot 6804+(-841)\cdot 1343$
Tonio