Question

prove that cube of any positive integer is in the of 4m,4m+2,4m+3 for integer m​

Answer 1

i hope so it will be help ful for u .

Answer 2

According to euclid's division lemma

a=bq+r so b=4

Let n be positive integer. Then it forms 4q ,4q+1

1. (4q)^3 =4(16q)^3 = 4m, where m=16q^3.
2. (4q+1)^3 =64q^3+48 a^2 +12q+1