[NT] 1. Mathematical Induction and Binomial theorem

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Practice problems

1. True or False

Justify: If $a$ and $b$ are relatively prime postiive integers, then the Diophantine equation $ax-by=c$ has infinitely many solutions in the positive integers.

##2. Solve the following problem by Alcuin of York, 775:
One hundred bushels of grain are distributed among 100 persons in such a way that each man receives 3 bushels, eash woman 2 bushels, and each child 1/2 bushel. How many men, women, and children are there?

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