Question Numbers 13 to 22 carry 3 marks each.gosative13. Show that any

1.	Question Numbers 13 to 22 carry 3 marks each.gosative13. Show that any positive odd integer is of the form Aq - 1 or Aq+3 wibem swa
Answer» Show that any positive odd integer is of the form 4q+1 or 4q+3 where q is some integer. Show that the square of an odd positive integer can be of the form 6q+1 or 6q+3 for some integer q. Prove that the square of any positive integer is of the form 3m or 3m+1. For any positive integers n, prove that n3-n is divisible by 6. Show that one and only out of n,n+4,n+8,n+12 and n+16 is divisible by 5, Where n is any positive integer. Write the prime factors of 546.

Question Numbers 13 to 22 carry 3 marks each.gosative13. Show that any positive odd integer is of the form Aq - 1 or Aq+3 wibem swa

Answer»

Show that any positive odd integer is of the form 4q+1 or 4q+3 where q is some integer.

Show that the square of an odd positive integer can be of the form 6q+1 or 6q+3 for some integer q.

Prove that the square of any positive integer is of the form 3m or 3m+1.

For any positive integers n, prove that n3-n is divisible by 6.

Show that one and only out of n,n+4,n+8,n+12 and n+16 is divisible by 5,

Where n is any positive integer.

Write the prime factors of 546.