Question

HELP ASAP

Answer 1

Answer: 231

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Work Shown:

$33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}$

Notice how 33*77 = 2541 and 11*231 = 2541

$2541 \equiv 1 \text{ (mod 508)}$ since 2541/508 has a remainder of 1.

So effectively $33*77 \equiv 1 \text{ (mod 508)}$ and $11*231 \equiv 1 \text{ (mod 508)}$