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Let R be a PID. Consider the Diophantine equation ax+by=N where a,b and N are integers and a,b are nonzero. Suppose x_0, y_0 is a solution: ax_0+by_0=N. Prove that the full set of solutions to this equation is given by
x = x_0 + (mb/gcd(a,b))
y = y_0 - (ma/gcd(a,b))
as m ranges over the integers.
Until recently, with the advent of cellular phones, modems, and pagers, the area codes in the United States and Canada followed a certain system
The manager of a weekend flea market knows from past experience that if he charges x dollars for a rental space at the flea market, then the number y of spaces he can rent is given by the equation y = 200 - 4x.
If a one person household spends an average USD 730 per week on groceries, calculate the minimum dollar amount spent per week for the middle 40 percent of one person households. Suppose that the standard deviation is USD 104 and the variable is norma..
Test BMI difference for all twin pairs
A boxing ring is in the shape of a square, 20 ft on each side. How far apart are the fighters when they are in opposite corners of the ring?
The probability of both receiving and not receiving an F. The grade distribution is as follows for the past three (3) years for a course in college algebra, as shown below.
The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
Suppose someone offers to pay you $100 if you draw 3 cards from a standard deck of 52 cards and all the cards are clubs. What should you pay for the chance to win
Probability that a player's pick wins the grand prize. In a certain lottery, k balls are chosen at random and without replacement from a bin containing N balls numbered 1 through N
The natural length of a spring is 10 cm. A force of 25 N stretches it to a length of 20cm. How much work, in units of N-cm, is done in stretching it from a length of 10cm to a length of 15cm?
what is the probability that each challenge will be won by a different camper? what is the Probability that Hank, one of the Seniors, will win at least one challenge?
If H and K are subgroup of G, with K a normal subgroup of G, K intersect H=1 and KH=G, then G is called a semidirect product (or split extention) of K by H.
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