Question

I'm stuck on problem 1 of assignment 2 Diophantine equations, what's the solution ?

Answer 1

Well, you have the equation \[6a + 9b + 20c = n\] and you have to find values of a,b and c while n is from 50 to 55. You can solve this in your head - try to divide n first by the greatest number - 20, check how many 20's you can have. Then check 9 similarly and then 6. You have to experiment a little bit.

Answer 2

6a + 9b + 20c = n.

50 isn't divisible by 3, and both 6 & 9 are, so you'll need at least 1 20. That leaves you with 30, which is 5*6, so a=5, b=0, c=1 is a solution for 50.

51 is divisible by 3; Trying 9s, you can see 9*6 = 54 is 3 past your target, so reduce the number of 9s by one and include a 6. a=1, b=5, c=0 is a solution for 51.

Similar fiddling will get you the others.

You could also write a program to try values of a, b, and c, and store combinations that get numbers in the range you want.