Use Euclidâ€™s algorithm to find HCF of 1190 and 1145. Express the HCF in the form 1190m + 1445n.

Prove that if x and y are both odd positive integers then x^2 + y^2 is even but not divisible by 4.

For any positive integer n, prove that \( n^3 \)- n is divisible by 6.

Show that any positive odd integer is of the form (4m + 1) or (4m + 3), where m is some integer.

Show that any positive odd integer is of the form (6m + 1) or (6m + 3) or (6m + 5), where m is some integer.