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

Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.

Use division algorithm to show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer

Prove that the square of an odd integer can be expressed in the form 8p + 1 where p = 0 or a positive integer.

Use division algorithm to show that the square of any positive integer is of the form 3p or 3p + 1.

The sum of the first 26 odd positive integers is

Show that one and only one out of n, n + 2 or n + 4 is divisible by 3, where n is any positive integer

Prove that the variance of the first n odd positive integers is the same as the variance of the first n event positive integers.

lf r, s, t are prime numbers and p, q are the positive integers such that their LCM of p,q is r^2 t^4 s^2, then the numbers of ordered pair of (p, q) is (A) 252 (B) 254 (C) 225 (D) 224

If (2+sqrt(3))^n=I+f, where I and n are positive integers and 0lt f lt1 , show that I is an odd integer and (1-f)(1+f) =1

For every positive integer n, prove that 7^(n) – 3^(n) is divisible by 4.