Question

show that any positive odd integer will be in form of 3n+1 or 3n+3 where is any integer.​

Answer 1

let x be any positive integer and n and r are its quotient and remainder and m=3

possible value of r is 1,2,3.

dividend= divisor*quotient+remainder

x=mn+r

put r =1

X=3n+1(odd)

put r =2

x=3n+2(even)

put r=3

x=3n+3(odd)

therefore, any positive odd integer will be in the form of 3n+1 or 3n+3