Question

Fill in the blanks and Make sure your answer is reduced.

Find inverse of 2 (mod 17).
2^-1 ≡ ____________(mod 17).

Find inverse of 34 (mod 89).
34^-1 ≡ _____________(mod 89).

Find inverse of 144 (mod 233).
144^-1 ≡ ___________(mod 233).

Find inverse of 200 (mod 1001).
200^-1 ≡ ___________ (mod 1001).

Fill in the blanks and If x has no solution, write "NA" on all the answer blanks.

Find all x such that 34x ≡ 77 (mod 89).
x ≡ ______ (mod ) _______

Find all x such that 144x ≡ 4 (mod 233).
x ≡ ______ (mod ) _______
Find all x such that 200x ≡13 (mod 1001).
x ≡ ______ (mod ) _______
Find all x such that 52x≡8 (mod 220).
x ≡ ______ (mod ) _______
Find all x such that 53x≡235 (mod 137).
x ≡ ______ (mod ) _______
Find all x such that 77x≡49 (mod 121).
x ≡ ______ (mod ) _______
Find all x such that 77x≡42 (mod 91).
x ≡ ______ (mod ) _______

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Answer 1

Find inverse of 2 (mod 17).
2^-1 ≡ 9 (mod 17).

Find inverse of 34 (mod 89).
34^-1 ≡ 55 (mod 89).

Find inverse of 144 (mod 233).
144^-1 ≡ 89 (mod 233).

Find inverse of 200 (mod 1001).
200^-1 ≡ 996 (mod 1001).

Fill in the blanks and If x has no solution, write "NA" on all the answer blanks.

Find all x such that 34x ≡ 77 (mod 89).
x ≡ 37 (mod ) 89

Find all x such that 144x ≡ 4 (mod 233).
x ≡ 123 (mod ) 233

Find all x such that 200x ≡13 (mod 1001).
x ≡ 936 (mod ) 1001

Find all x such that 52x≡8 (mod 220). == 13x ≡ 2 (mod 55)
x ≡ 34 (mod ) 55

Find all x such that 53x≡235 (mod 137).
x ≡ 113 (mod ) 137

Find all x such that 77x≡49 (mod 121).
x ≡ NA. Because inverse of 77 (mod 121) doesn't exist. Or gcd of 77 and 121 is 11 which is not equal to gcd

Find all x such that 77x≡42 (mod 91). == 11x ≡ 6 (mod 13)
x ≡ 10 (mod ) 13