UNIT IV DIOPHANTINE EQUATIONS AND CONGRUENCES

The inverse of 3 modulo 7 is?

• -1

• -2

• -3

• -4

What is the inverse of 7 modulo 26?

• 12

• 14

• 15

• 20

Given x ≡ 11(mod 8):

Which of the following integers are valid solutions for x?

• -43

• -17

• 15

• 42

• None of the above

What is the solution of the linear congruence 4x ≡ 5 (mod 9) ?

• 6 (mod 9)

• 8 (mod 9)

• 9 (mod 9)

• 2 (mod 9)

The unique solution of the linear congruence ax ≡ b (mod m), where (a, m)=1 is the least residue of

• a^-1b (mod m)

• ab^-1 (mod m)

• ab (mod m)

• None of the above

Which of the following the condition is valid, for the linear congruence ax ≡ b (mod m) to be solvable, where d=(a, m)

• d|b

• d|a

• d|m

• None of the above

How many incongruent solutions are there for the linear congruence ax ≡ b (mod m), when d=(a, m) divides b

• b

• a

• d

• m

The linear congruence ax ≡ b (mod m) has unique solution if and only if

• (a, m)=1

• (a, m)=d

• (b, m)=1

• (b, m)=d

The number of incongruent solutions of 48x ≡ 144 (mod 84) is

• 4

• 6

• 12

• 24

The incongruent solution of the linear congruence 5x ≡ 3 (mod 6) is

• x ≡ 5 (mod 6)

• x ≡ 4 (mod 6)

• x ≡ 2 (mod 6)

• x ≡ 3 (mod 6)