Question

A = {2x+1: x ∈ N and x < 2020}, and B = {a(b+1)^3 : a,b ∈ N}.

Find | A ∩ B |

Answer 1

m um Note that A={3,5,7,.---, 4039} odd numbers from 3 to 4039, B= { a cbr13: ating bt no} For pdt of two numbers to be odd, both should be odd. for btl to be odd, b should be even. So we take even numbers b= 2,4,6,--.. For a particular b, a runs from 1 to a certain number (say No) through odd numbers. we can determine No explicitly. p 4031 / 5.7 denotes Let ne r 40397 E (6+)3) greatest integer y function

We call - 40397 1 4 6 n Let [. ] denotes greatest integer 3) greater action N= {n ni if n is odd if n is even. observe, is² = 3375 17²=4913 clearly, b takes 2,4,6, --,14 for each b, a takes 1,3,5,--, Ny where No can be determined as above. : These are the numbers in AMB which can be explicitly determined as above.