Let a, b, m be positive integers. Choose correct statement(s). Select one or more:a.a ≡ b (mod m) if and only if m|(a-b)b.The expression "a|b" means a is a multiple of b.c.The expression "a ≡ b (mod m)" means a  and b are both multiples of md.The expression "a|b" means b is a multiple of a.

or all integers a, b, c, m with m > 0 and c > 0, if a ≡ b (mod m) then ac ≡ bc (mod mc)

For all integers a, b, c, m with m > 0 and c > 0, if ac ≡ bc (mod m), then a ≡ b (mod m

5. Find a div m and a mod m whena) a = −111, m = 99. b) a = −9999, m = 101.c) a = 10299, m = 999. d) a = 123456, m = 1001.6. Decide whether each of these integers is congruent to 5 modulo 17.a) 80 b) 103 c) −29 d) −1227. Find each of these values.a) (992 mod 32)3 mod 15 b) (34 mod 17)2 mod 11c) (193 mod 23)2 mod 31 d) (893 mod 79)4 mod 268. Convert the decimal expansion of each of these integers to a binary expansion.a) 23 b) 45 c) 241 d) 10259. Convert the binary expansion of each of these integers to a decimal expansion.a) (1 1011)2 b) (10 1011 0101)2c) (11 1011 1110)2 d) (111 1100 0001 1111)2

Let n ∈ N and a, b, c ∈ Z. Recall that c mod n is the remainder r ∈{0, 1, . . . , n − 1} on division of c by n. Provide a short proof that ifa mod n = b mod n, then a ≡ b mod n.2

The % or modulus operator returns the remainder from dividing two numbers.Question 3Select one:TrueFalse