- Diophantine Equations,
a selection of answers from the Dr. Math archives.
- Diophantine Equations
- We have searched the Web for information about Diophantine
- 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
- Solve this system: 187y+98x+45z=48; 2y+9x+3z=198.
- Linear Diophantine Equation
- Given positive integers a and b such that a|b^2, b^2|a^3, a^3|b^4,
b^4|a^5,....., prove that a = b.
- Solving Multivariable Diophantine
- 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 ax-by = c has infinitely many solutions in the positive
- 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?
- Second-Degree Two-Variable Diophantine
- Solve Ax^2+Bxy+Cy^2+Dx+Ey+F = 0 where B^2-4AC=k^2 for some integer k.
- Linear Diophantine Equations
- ...how was the t-variable 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?