Question

Since 0 <r<4, the possible remainders are 0, 1, 2 and 3.
That is, a can be 4q, or 4q+1, or 4q+2, or 49 +3, where q is the quotient.
since a is odd, a cannot be 4 or 4q+2 (since they are both divisible by 2).
Therefore, any odd integer is of the form 49 + 1 or 4q+3.
EXERCISE - 1.1
1.
Use Euclid's division algorithm to find the HCF of
(i) 900 and 270
(ii) 196 and 38220 (iii) 1651 and 2032
2.
Use Euclid division lemma to show that any positive odd integer is of the for
69 + 3 or 69 +5, where q is some integers.
3
Use Euclid's division lemma to show that the square of any positive integer
3p, 3p+1.
Use Euclid's division lemma to show that the cube of any positive integer i​

Answer 1

attach picture also so that we can understand better