Question

Write cubes of five natural number of the form 3 n + 1 (example 4 7 10) and verify that the cube of the natural number of the form 3n+ 1 is natural number of same form

Answer 1

if any integer is divided by 3 , possible reminders are 0,1,2

when remainder is 0 , a= 3q , a³= 27q³ , 3(9q³) which is in the form 3n

when remainder is 1, a= 3q+ 1 , a³=27q³+1+27q²+9q

= 3( 9q³+9q²+3q) +1 in the form 3n+1

similarly in remainder 2 also..