Mathematics 566 Homework (due Nov 15th) D&F;7.4: D&F;7.6:

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Mathematics 566
Homework (due Nov 15th)
A. Hulpke
D&F;7.4: 5,7,9,11∗ ,17
D&F;7.6: 1,5,6∗
D&F;8.2: 1,3,5
1) [Ch’in Chiu-Shao, 1202-1261] Three farmers divide equally the rice they have grown. One goes to a
market where an 83-pound weight is used, another to a market that uses a 110-pound weight, and the
third to a market that uses a 133-pound weight. Each farmer sells as many full measures as possible, and
when they return home, the first has 32 pounds of rice left, the second 70 pounds, and the third 128
pounds. Find the total amount of rice they took to the market.
(Note: The original problem has a 135-pound weight and remainder 30 (replacing the 135/30 pound
values). In this case the moduli are not coprime, so the homomorphism analoguous to the Chinese
remainder theorem is not surjective. However one can still find a preimage unique modulo the lcm of the
moduli.)