karimok's blog

very useful problem
By karimok, history, 8 years ago, translation, In English

Hello everybody)

help me with problem

we looking for quantity of integer solutions (x,y) equation ; |a|,|b| <=

  • Vote: I like it
  • +5
  • Vote: I do not like it

»
8 years ago, # |
← Rev. 2   Vote: I like it 0 Vote: I do not like it

I found this:

a.y + b.x = x.y

b.x = y.(x-a)

y=(b.x) / (x-a);

x,y are integers so (a|b means b%a=0)

x-a| b.x

x-a| b.x — b.(x-a)

x-a| b.x — b.x + a.b

x-a| a.b

for every z (z|a.b) there is an integer pair (x,y) suitable to all conditions. So the answer is same with quantity of divisors of a.b

→ Reply