Question

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

integer.

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

for some integer q.

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

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

Q. 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.

Q. Write the prime factors of 546.

Answer 1

I don't know 3, 4 and 5.
(6)
Prime factorization of 546= 2*3*7*13