Question 2 Make sure that all your answers are explained carefully. (a) Find the remainder of 117 when divided by 22. (b) A billionaire has built a rocket to fly to the moon. At what time will he land on the moon, if he lifts off at 7 am and lands 68 hours later? (c) Find a negative integer n that satisfies n = 312 mod 9. (d) Is a = 4441117773388123 divisible by 11? (e) Let p = 3 mod 5 be a prime number. Solve the system of congruences x = 1 mod 5 x = 512 mod p

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