Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r.
`a = 13 , b = 3`

Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 132, b = 11

Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 125 , b = 5

Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 80 , b = 8

Find the HCF and LCM of the pairs of integers and verify that LCM (a, b) xx HCF (a, b) = a xx b . (a) 16 and 80 (b) 125 and 55

a and b are positive integers such that a^3 - b^2 is a prime number. Then a^2 - b^2=

Euclids Division Lemma states that for any two positive integers a and b, there exists unique integers q and r such that a=bq+r , where r must satisfy.

If r = 0, then what is the relationship between a, b and q in a = bq + r ?

In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step. 5. If a and b positive integers, then you know that a =bq +r, 0 £ r lt b , where q is a whole number. Prove that HCF (a,b) =HCF (b,r).

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax+b)/(px^(2)+qx+r)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (px^(2)+qx+r)/(ax+b)