We consider the online scheduling on an unbounded (dropline) parallel batch machine to minimize the time by which all jobs have been delivered In this paper, all jobs arrive over time and the running batches are allowed limited restart Here limited restart means that a running batch which contains restarted jobs cannot be restarted again A dropline parallel batch machine can process. Homework Statement This is a question from the book I'm studying called 'Mathematical Proofs A transition to advanced mathematics' Homework Equations Let a, b, n be integers, with n≥2 Prove that if a\\equivb(mod n), then a2\\equivb2(mod n) The Attempt at a Solution Following the examples. 0 (mod 4) 1 (mod 4) 213 If a;b are integers such that a b (mod p) for every positive prime p, prove that a = b Proof Since the set of prime numbers in Z is in nite, we can always nd a prime number p larger than any given number In particular we can nd a prime number p such that 0 ja bj< p Now by hypothesis, we have, for this prime p, a.
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