Manipur Board Solutions for Chapter: Number System, Exercise 1: EXERCISE 1.1

Show that every integer is of the form $4q,4q+1,4q+2 or 4q-1$.

Show that the product of three consecutive integers is divisible by $6$.

Show that the square of an odd integer is of the form $8k+1$.

If $a$ is divisible by neither $2$ nor $3$, show that $a^2-1$ is divisible by $24$.

Show that any square number cannot be put in the form $4k+2$.

Show that any square number is of the form $3n$ or $3n+1$.

Show that one of three consecutive odd integers is a multiple of $3$.

Show that the product of any three consecutive even integers is divisible by $48$.