See if http://en.m.wikipedia.org/wiki/Modular_multiplicative_inverse helps.cloveryeah said:Homework Statement
1007n+1703m=1 when n and m are integers
Homework Equations
The Attempt at a Solution
i hv tried for so many times, but i can't find it
the GCD of 1007 and 1703 is 1, so it is possible to find n and m
cloveryeah said:Homework Statement
1007n+1703m=1 when n and m are integers
Homework Equations
The Attempt at a Solution
i hv tried for so many times, but i can't find it
the GCD of 1007 and 1703 is 1, so it is possible to find n and m
The purpose of finding a combination of n and m is to determine the number of possible arrangements or selections of objects from a set of n objects, taking m objects at a time. This can help in solving various mathematical and scientific problems, such as probability calculations, counting permutations and combinations, and optimizing experimental designs.
To find a combination of n and m, you can use the formula n! / (m!(n-m)!), where n is the total number of objects and m is the number of objects being selected. This formula is also known as the combination formula. Alternatively, you can use a combination calculator or a computer program to quickly calculate the combination.
A combination is an arrangement of objects where the order of the objects does not matter, whereas a permutation is an arrangement where the order does matter. In other words, combinations are selections without replacement, while permutations are selections with replacement. For example, selecting three different fruits from a basket would be a combination, while selecting three fruits in a specific order would be a permutation.
No, the formula for combinations n! / (m!(n-m)!) only works for selecting distinct objects. If there are repeating elements, you would need to adjust the formula accordingly. For example, if there are n total objects with x identical elements, the formula would be n! / (x!(m-x)!(n-m)!).
Finding a combination of n and m is commonly used in various fields such as mathematics, statistics, computer science, chemistry, and genetics. It is used to model real-world situations, make predictions, and solve problems. For example, in genetics, combinations are used to calculate the number of possible genotypes and phenotypes in a population.