Quiz (Linear Diophantine Equations)

(1) Which of the following Diophantine equations cannot be solved?

    (a)
    
    (b)
    
    (c)

(2) Determine all solutions in the integers of the following Diophantine equations:

    (a)
    
    (b)
    
    (c)

(3) Determine all solutions in the positive integers of the following Diophantine equations

    (a)
    
    (b)
    
    (c)

(4) When Mr. Smith cached a check at his bank, the teller mistook the number of cents for the number of dollars and vice versa. Unaware of this, Mr. Smith spent 68 cents and then noticed to his surprise that he had twice the amount of the original check. Determine the smallest value for which the check could have been written.

(5) Divide 100 into two summands such that one is divisible by 7 and the other by 11.

(6) Is it possible to have 50 coins, all of which are pennies, dimes, or quarters, with a total worth

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Linear Diophantine Equations Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/linear-diophantine-equations-quiz.html