Find the number of positive integers <1000 that can be expressed as 2k−2m, where k and m are non-negative integers.

How to solve this?

1

2k-2m=2(k-m)=2a...(a>0)=even number=2,4,6......998
total nos. are=n-1=996/2
                     =>n=499 (ANS)

 the no. of positive int. <1000 are 499.

is the ans 500*500?? its given tat 2k-2m<1000 , so k-m<500

now as both k&m are non negative integers, the possibilities of both k & m are from 0 to 499.

so for value of k v have500 possibilities of m

so for 500 values of k v hav 500*500 possibilities of m

hence i think the ans is (500)^2

dear Siddhant,500*500=2500>1000

acording to me the asnwer should be 499