 Diophantine Equations,
a selection of answers from the Dr. Math archives.
 Diophantine Equations
 We have searched the Web for information about Diophantine
equations.
 Diophantine Equations, Step by Step
 Find all positive integer solutions to 43x + 7y + 17z = 400.
 Integer Solutions of ax + by = c
 Given the equation 5y  3x = 1, how can I find solution points where
x and y are both integers? Also, how can I show that there will always be
integer points (x,y) in ax + by = c if a, b and c are all integers?
 Buying Cows, Pigs, and Chickens
 A farmer buys 100 animals for $100. The animals include at least one cow,
one pig, and one chicken. If a cow costs $10, a pig costs $3, and a chicken
costs $0.50, how many of each did he buy?
 How Many Mice, Cats, and Dogs?
 You must spend $100 to buy 100 pets, choosing at least one of each pet.
The pets and their prices are: mice @ $0.25 each, cats @ $1.00 each, and
dogs @ $15.00 each. How many mice, cats, and dogs must you buy?
 Money Puzzle
 A man goes to the bank and asks for x dollars and y cents.
 Systems with More Variables than
Equations
 Solve this system: 187y+98x+45z=48; 2y+9x+3z=198.
 Linear Diophantine Equation
 Given positive integers a and b such that ab^2, b^2a^3, a^3b^4,
b^4a^5,....., prove that a = b.
 Solving Multivariable Diophantine
Equations
 Finding general solutions to two diophantine equations.
 Diophantine Equations, Apples, Bananas
 Mick has $5.63 worth of bananas and apples. Bananas are 13 cents each
and apples are 7 cents each. How many different combinations of apples
and bananas can he have and what are they?
 Diophantine equations in Number Theory
 If a and b are relatively prime positive integers, prove that the
Diophantine equation axby = c has infinitely many solutions in the positive
integers.
 All Possible Solutions: Diophantine Equations
 Lance and Mario sold hot dogs for $1.65, hamburgers for $2.35, sodas for $.85,
and a combo plate with fries, salad, a hamburger, and soda for $3.89. They
sold 80 items in an hour for $163.24. How many of each kind of food did
they sell, and how much did they make on each kind of food?
 SecondDegree TwoVariable Diophantine
Equation
 Solve Ax^2+Bxy+Cy^2+Dx+Ey+F = 0 where B^24AC=k^2 for some integer k.
 Linear Diophantine Equations
 ...how was the tvariable introduced, and what is the general method?
 Positive Unit Fractions
 Find five different positive unit fractions whose sum is 1.
 Switching Dollars and Cents
 How do I find an equation?
