Let z denote the set of all integers and A={(a,b) :a^2 + 3b^2=28 , ab belongs to Z}

and B={(a,b): ab , ab belongs to Z} then n(A∩B)=??

Question

Let z denote the set of all integers and A={(a,b) :a^2 + 3b^2=28
, ab belongs to Z}
and B={(a,b): ab , ab belongs to Z} then n(A∩B)=??

Prasanta · Accepted Answer

A=a, b: a2+3b2=28
⇒A=1, 3, 4, 2, 5, 1, -1, 3, -4, 2, -5, 1, 1, -3, 4, -2, 5, -1, -1, -3, -4, -2, -5, -1

B=a, b: ab, ab∈Z
⇒B=all ordered pairs of integers

So, we see that A∩B=A
⇒nA∩B=nA=12